Question

Find the derivative f'(x) using the product, chain, and natural exponential rules.

$$\begin{array}{l} \displaystyle \text{if } y = f(g(x)),\ y' = f'(g(x))\cdot g'(x) \[12pt] \displaystyle f(x) = (3x + 4)^{-2}\left(5e^{x}\right) \end{array}$$

Accepted Answer

$$f'(x) = -6(3x + 4)^{-3}\left(5e^{x}\right) + (3x + 4)^{-2}\left(5e^{x}\right)$$

Answer

$$f'(x) = -6(3x + 4)^{-3}\left(5e^{x}\right) - (3x + 4)^{-2}\left(5e^{x}\right)$$

Answer

$$f'(x) = -6(3x + 4)^{-3}\left(5e^{x}\right)$$

Answer

$$f'(x) = (3x + 4)^{-2}\left(5e^{x}\right)$$

Derivative Rules - Multi Chain Product Natural Exponential (with Rule) to Derivative

Practice:

Derivative Rules - Multi Chain Product Natural Exponential (with Rule) to Derivative