# All pages

- Abel's theorem on convergence of power series
- Absolute value function
- Absolute value of sine function
- Absolutely convergent series
- Accelerated gradient method
- Additively asymptotic functions
- Additively separable function
- Algebra containing all functions of a given algebra containing the identity function and their antiderivatives contains all their iterated antiderivatives
- Alternating series theorem
- Alternating series theorem fails if signs are not strictly alternating
- Alternating series theorem fails if terms are not monotonically decreasing in magnitude
- Analogue of alternating series theorem if magnitude of terms approaches a positive number
- Approximate Newton's method for optimization of a function of multiple variables
- Approximate Newton's method with constant approximate inverse Hessian
- Arc sine function
- Arc tangent function
- Automatic differentiation
- Autonomous delay differential equation
- Basic comparison test
- Bernoulli differential equation
- Bisection method
- Broyden's method for optimization of a function of multiple variables
- Broyden's method for root-finding for a vector-valued function of a vector variable
- Chain rule for differentiation
- Chain rule for higher derivatives
- Chain rule for partial differentiation
- Change of variable substitution
- Circular trap with integration by parts
- Clairaut's equation
- Clairaut's theorem on equality of mixed partials
- College:Product rule for differentiation
- Composite of any function with even function is even
- Composite of even function with odd function is even
- Composite of increasing functions is increasing
- Composite of odd functions is odd
- Composite of two functions
- Concavity of a function
- Concept of equality conditional to existence of one side
- Condition number
- Continuous function
- Continuous functions form a unital algebra
- Continuous functions form a vector space
- Continuous in every linear direction not implies continuous
- Continuous partials implies differentiable
- Continuous partials of a given order implies differentiable that many times
- Conversion of a differential equation to a system of first-order differential equations
- Coordinate descent
- Cosecant function
- Cosine-cubed function
- Cosine-squared function
- Cosine function
- Cosine of square function
- Cotangent function
- Critical point
- Critical point for a function of multiple variables
- Cube function
- Degree difference test
- Delay differential equation
- Derivative
- Derivative of differentiable function need not be continuous
- Derivative of differentiable function satisfies intermediate value property
- Derivative of power series
- Difference quotient
- Differentiable function
- Differentiable functions form a vector space
- Differential equation
- Differentiation is linear
- Differentiation rule for piecewise definition by interval
- Differentiation rule for power functions
- Directional derivative
- Discrete derivative
- Divided differences
- Domain
- Even function
- Even part
- Existence of directional derivatives in every direction not implies differentiable
- Existence of partial derivatives not implies differentiable
- Explicit differential equation
- Exponent shift method for power series summation
- Extreme value theorem
- Factorization method for solving differential equations
- Failure of Clairaut's theorem where both mixed partials are defined but not equal
- Failure of Clairaut's theorem where only one of the mixed partials is defined
- False position method
- Fifth power of sine function
- Finite difference
- First-degree differential equation
- First-order differential equation
- First-order exact differential equation
- First-order first-degree autonomous differential equation
- First-order first-degree differential equation
- First-order homogeneous linear discrete delay differential equation with constant coefficients
- First-order linear differential equation
- First derivative test
- First derivative test and one-sided derivative test are incomparable
- First derivative test fails for function that is discontinuous at the critical point
- First derivative test for a function of multiple variables
- First derivative test is conclusive for differentiable function at isolated critical point
- First derivative test is conclusive for function with algebraic derivative
- First derivative test is conclusive for locally analytic function
- First derivative test is inconclusive for function whose derivative has ambiguous sign around the point
- Formula for even and odd part of power series
- Fractional part
- Fredholm equation of the first type
- Freshman product rule
- Fresnel cosine integral
- Fresnel sine integral
- Function
- Gamma function
- Germ of a function
- Globally analytic function
- Golden ratio
- Gradient descent
- Gradient descent using Newton's method
- Gradient descent with constant learning rate
- Gradient descent with constant learning rate for a L1-regularized quadratic function of one variable
- Gradient descent with constant learning rate for a convex function of one variable
- Gradient descent with constant learning rate for a logistic log-loss function of one variable
- Gradient descent with constant learning rate for a quadratic function of multiple variables
- Gradient descent with constant learning rate for a quadratic function of one variable
- Gradient descent with decaying learning rate
- Gradient descent with exact line search
- Gradient descent with exact line search for a quadratic function of multiple variables
- Gradient descent with optimal constant learning rate converges quadratically from sufficiently close to a minimum of multiplicity one
- Gradient vector
- Graph of a function of multiple variables
- Graph of a function of two variables
- Greatest integer function
- Grünwald–Letnikov derivative
- Hessian matrix
- Hessian matrix defines bilinear form that outputs second-order directional derivatives
- Higher-order finite difference
- Higher derivative
- Higher derivative test
- Higher derivative test is conclusive for function with algebraic derivative
- Higher derivative test is conclusive for locally analytic function
- Higher derivative test need not be conclusive for infinitely differentiable function at isolated critical point
- Hill climbing optimization
- Homogeneous linear differential equation with constant coefficients
- Homogeneous linear discrete delay differential equation with constant coefficients
- Horizontal asymptote
- Hyperbolic cosine function
- Hyperbolic sine function
- Increasing and differentiable implies nonnegative derivative that is not identically zero on any interval
- Increasing function
- Increasing functions form a cone in a vector space
- Infinitely differentiable function
- Initial value problem
- Integer point of local extremum not implies point of local extremum among integers
- Integral test
- Integration and differentiation method for power series summation
- Integration by parts
- Integration by parts involving a function that is zero on the boundary
- Integration by substitution
- Integration of linear transform of function
- Integration of quotient of derivative of function by function
- Integration of rational function whose denominator has distinct linear factors
- Integration of rational function with quadratic denominator
- Integration rule for piecewise definition by interval
- Intermediate value property
- Intermediate value theorem
- Inverse function integration formula
- Inverse function of odd function is odd
- Inverse function theorem
- Inverse hyperbolic cosine function
- Inverse hyperbolic sine function
- Inverse logistic function
- Inverse of increasing function is increasing
- Jacobian matrix
- L1-regularization may change the quadrant of local minimum for a quadratic function of two variables
- L1-regularized quadratic function
- L1-regularized quadratic function of multiple variables
- L1 norm
- Lagrange equation
- Lagrange mean value theorem
- Leibniz integral rule
- Limit
- Limit comparison test
- Limit is linear
- Limit is multiplicative
- Limit of quotient equals quotient of limits
- Line search
- Linear differential equation
- Local maximum from the left implies left hand derivative is nonnegative if it exists
- Local maximum value may be smaller than local minimum value
- Local search
- Locally analytic function
- Locally analytic not implies globally analytic
- Logarithmic derivative
- Logarithmic scoring rule
- Logarithmic scoring rule is proper
- Logarithmic scoring rule is the only proper scoring rule up to affine transformations in case of more than two classes
- Logistic function
- Logistic log-loss function of one variable
- Main Page
- Max-estimate version of Lagrange remainder formula
- Mean value theorem
- Meaning of partial derivative depends on entire coordinate system
- Multiplicatively separable function
- Natural logarithm of absolute value of sine function
- Nesterov's accelerated gradient descent with constant learning rate for a quadratic function of one variable
- Nesterov's gradient acceleration
- Newton's method converges linearly from sufficiently close to a root of finite multiplicity greater than one
- Newton's method converges quadratically from sufficiently close to a root of multiplicity one
- Newton's method for optimization of a function of multiple variables
- Newton's method for optimization of a function of one variable
- Newton's method for optimization of a logistic log-loss function of one variable
- Newton's method for quadratic functions
- Newton's method for root-finding for a function of one variable
- Newton's method for root-finding for a vector-valued function of a vector variable
- Non-linear least squares
- Nonnegative derivative that is not identically zero on any interval implies increasing
- Notational confusion of multivariable derivatives
- Numerical differentiation
- Odd function
- Odd part
- Odd positive power function
- Odd positive power of sine function
- One-sided derivative test
- One-sided version of higher derivative test
- One-sided version of second derivative test
- Padé approximant
- Parallel coordinate descent
- Parametric derivative
- Partial derivative
- Peano existence theorem
- Piecewise definition of function
- Point of absolute extremum
- Point of local extremum
- Point of local extremum among integers
- Point of local extremum implies critical point
- Point of local extremum implies critical point for a function of multiple variables
- Pointwise product of functions
- Positive derivative implies increasing
- Positive part function
- Positive part of sine function
- Power series solution method for differential equations
- Power series summation operator is linear
- Procedure for finding absolute extrema for a continuous function on a closed bounded interval
- Procedure for finding local and endpoint extrema using the first derivative test
- Procedure for finding local and endpoint extreme values using the higher derivative test
- Procedure for local and endpoint extrema among integers using the first derivative test
- Product of increasing functions need not be increasing
- Product rule for differentiation
- Product rule for differentiation of dot product
- Product rule for higher derivatives
- Product rule for higher partial derivatives
- Product rule for partial differentiation
- Proof of chain rule for differentiation
- Proof of product rule for differentiation using chain rule for partial differentiation
- Quadratic formula
- Quadratic function
- Quadratic function of multiple variables
- Quotient rule for differentiation
- Radius of convergence
- Radius of convergence of derivative of power series equals radius of convergence
- Range
- Rate of convergence
- Rational functions can be repeatedly integrated within elementarily expressible functions
- Real number
- Receiver operating characteristic
- Reciprocal function
- Recursive version of integration by parts
- Relation between Hessian matrix and second-order partial derivatives
- Relation between gradient vector and directional derivatives
- Relation between gradient vector and partial derivatives
- Relative logarithmic derivative
- Repeated differentiation is linear
- Repeated use of integration by parts
- Riemann series rearrangement theorem
- Rolle's theorem
- Root-finding algorithm
- Root test
- Rules for determining interval of convergence of power series
- Rules for determining interval of convergence of power series of rational function
- Sandbox
- Secant-cubed function
- Secant-squared function
- Secant function
- Secant method
- Secant method converges with order equal to the golden ratio from sufficiently close to a root of multiplicity one
- Second-order differential equation
- Second-order first-degree autonomous differential equation
- Second-order mixed partial derivative
- Second derivative
- Second derivative rule for inverse function
- Second derivative rule for parametric descriptions
- Second derivative test
- Second derivative test for a function of multiple variables
- Second derivative test for a function of two variables
- Second derivative test is not stronger than first derivative test
- Second derivative test operates via first derivative test
- Separable differential equation
- Separable function
- Separately continuous function
- Separately continuous not implies continuous
- Sequence
- Series summation of rational function with quadratic denominator
- Signum function
- Signum vector function
- Sinc-cubed function
- Sinc-squared function
- Sinc function
- Sine-cubed function
- Sine-squared function
- Sine function
- Sine integral
- Sine of reciprocal function
- Sine of square function
- Single-step autonomous delay differential equation
- Sinusoidal function
- Slope-based root-finding method
- Spectral norm
- Square function
- Substitution method for power series summation
- Substitution method for solving differential equations
- Summary table of multivariable derivatives
- Tanc function
- Tangent-cubed function
- Tangent-squared function
- Tangent function
- Tangent line
- Taylor polynomial
- Taylor series
- Taylor series of a function may converge to another function that agrees with it only at the center
- Taylor series of polynomial is the same polynomial
- Taylor series operator commutes with composition
- Taylor series operator commutes with differentiation
- Taylor series operator is linear
- Taylor series operator is multiplicative
- Uniformly bounded derivatives implies globally analytic
- Uniqueness theorem for limits
- Using the product rule for differentiation for limiting behavior at points with undefined derivative
- Value of partial derivative depends on all inputs
- Variation of first derivative test for discontinuous function with one-sided limits
- Vertical line test
- Wronskian of two functions
- Zero derivative implies locally constant
- Zeta function