Derivatives and the Chain Rule

The
Chain Rule

The Chain Rule of Differentiation

​Taking the derivative of a composite function.

​Ex: f(x) = (3x + 1)²

​Ex: f(x) = (x² + 5)⁴

Math Response

Find the derivative of the following:

$$y=2\left(4x-7\right)^3$$

Type answer here

Correct Answer: 24\left(4x-7\right)^2

Deg^°

Rad

Math Response

Find the derivative of the following:

$$f\left(x\right)=\frac{1}{\sqrt[3]{5x-3}}$$

Type answer here

Correct Answer: \frac{-5}{3\sqrt[3]{\left(5x-3\right)^4}}

Deg^°

Rad

Math Response

Evaluate:

$$f\left(x\right)=2x\sqrt[]{1-x}$$

Find f'(-3)

Type answer here

Correct Answer: \frac{11}{2}

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Rad

Find f'(4) given the following:

g(4) = 4 & g'(4) = -2
h(4) = 9 & h'(4) = 5

​Find: f(x) = (g(x))²

Math Response

Find f'(4) given the following:

g(4) = 4 & g'(4) = -2

h(4) = 9 & h'(4) = 5

$$f\left(x\right)=\sqrt[]{h\left(x\right)}$$

Type answer here

Correct Answer: \frac{5}{6}

Deg^°

Rad

Math Response

Find f'(4) given the following:

g(4) = 4 & g'(4) = -2

h(4) = 9 & h'(4) = 5

$$f\left(x\right)=h\left(g\left(x\right)\right)$$

Type answer here

Correct Answer: -10

Deg^°

Rad