Question

Differentiating Exponential functions In Exercise,find the derivative of the function. See Example 2 and 3.

y = e^-x2

Answer 1

Answer:
`-2xe^(-x^2)`

Explanation:

Let u be a differentiable function , then

`(d)/(dx)(e^x)=e^x`

`(d)/(dx)e^u=e^u(du)/(dx)` (1)

Given function :
`y = e^(-x^2)`

Differentiate both sides with respect to x , we get

`y'=e^(-x^2)(d(-x^2))/(dx)` (By using (1))

`\Rightarrow\ y'=e^(-x^2)(-2x)` [∵
`(d)/(dx)(x^n)=x^(n-1)`]

`\Rightarrow\ y'=-2xe^(-x^2)`

Hence, the derivative of the given function is
`-2xe^(-x^2)` .