Question

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

Answer 1

`(dF(x))/(dx) =20e^(4x)-6x^5e^{x^(-6)}`

Explanation:

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

`(dF(x))/(dx)=(d)/(dx) [(5e^(4x))+(e^(-x^6))]`

`(dF(x))/(dx)=(d)/(dx) [(5e^(4x))]+(d)/(dx) [(e^(-x^6))]`

`(dF(x))/(dx)=5(d)/(dx) [(e^(4x))]+(d)/(dx) [(e^(-x^6))]`

using the chain rule we find that

`(d)/(dx) [(e^(4x))]= (d)/(d(4x)) [(e^(4x))]+ (d)/(dx) [4x] = 4e^(4x),`

`(d)/(dx) [(e^(-x^6))] = (d)/(d(-x^6)) [(e^(-x^6))]+(d)/(dx) [(-x^6})]= -6x^5e^(-x^6);`

therefore,

`(dF(x))/(dx)=5(d)/(dx) [(e^(4x))]+(d)/(dx) [(e^(-x^6))] =5(4e^(4x))-6x^5e^{x^(-6)}`

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