Question

What is the derivative of this function: F(x)=(5e^4x)+(e^-x^6)

Answer 1

Answer:

$\dfrac{dF(x)}{dx} =20e^{4x}-6x^5e^{x^{-6}}$

Step-by-step explanation:

The derivative of $F(x)$ is calculated as follows:

$\dfrac{dF(x)}{dx}=\dfrac{d}{dx} [(5e^{4x})+(e^{-x^6})]$

$\dfrac{dF(x)}{dx}=\dfrac{d}{dx} [(5e^{4x})]+\dfrac{d}{dx} [(e^{-x^6})]$

$\dfrac{dF(x)}{dx}=5\dfrac{d}{dx} [(e^{4x})]+\dfrac{d}{dx} [(e^{-x^6})]$

using the chain rule we find that

$\dfrac{d}{dx} [(e^{4x})]= \dfrac{d}{d(4x)} [(e^{4x})]+ \dfrac{d}{dx} [4x] = 4e^{4x},$

$\dfrac{d}{dx} [(e^{-x^6})] = \dfrac{d}{d(-x^6)} [(e^{-x^6})]+\dfrac{d}{dx} [(-x^6})]= -6x^5e^{-x^6};$

therefore,

$\dfrac{dF(x)}{dx}=5\dfrac{d}{dx} [(e^{4x})]+\dfrac{d}{dx} [(e^{-x^6})] =5(4e^{4x})-6x^5e^{x^{-6}}$

$\boxed{\dfrac{dF(x)}{dx} =20e^{4x}-6x^5e^{x^{-6}}}$