Quiz:Chain rule for differentiation

From Calculus

See chain rule for differentiation and chain rule for higher derivatives for background information.

See Quiz:Differentiation rules for a quiz on all the differentiation rules together.

Formulas

General difficulty level of questions in this section: College level (unless otherwise specified).

1 Suppose and are both twice differentiable functions everywhere on . Which of the following is the correct formula for , the second derivative of the composite of two functions?

2 Suppose are everywhere differentiable functions from to . What is the derivative where denotes the composite of two functions? In other words, .

3 Suppose is a differentiable function from to and are such that and . What is the value of , where denotes the composite of two functions and occurs times in the expression, with ?