Vipul: Created page with "==Statement== Suppose $f$ is a function of two variables $x,y$ and $f$ and its partial derivative $\partial f/\partial x$ are ..."

2012-02-13T00:30:38Z

Created page with "==Statement== Suppose <math>f</math> is a function of two variables <math>x,y</math> and <math>f</math> and its partial derivative <math>\partial f/\partial x</math> are ..."

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==Statement==

Suppose <math>f</math> is a function of two variables <math>x,y</math> and <math>f</math> and its [[partial derivative]] <math>\partial f/\partial x</math> are both [[continuous function]]s on an interval of the form <math>[x_1,x_2] \times [y_1,y_2]</math>. Then, for <math>x \in (x_1,x_2)</math>, we have:

<math>\frac{d}{dx} \int_{y_1}^{y_2} f(x,y) \, dy = \int_{y_1}^{y_2} \frac{\partial}{\partial x} f(x,y) \, dy</math>

Leibniz integral rule - Revision history

Vipul: Created page with "==Statement== Suppose f is a function of two variables x,y and f and its partial derivative \partial f/\partial x are ..."

Vipul: Created page with "==Statement== Suppose $f$ is a function of two variables $x,y$ and $f$ and its partial derivative $\partial f/\partial x$ are ..."