Question

Differentiating Exponential Functions In Exercise, find the derivative of the function.

y = 4e^x2

Answer 1

Answer:
`8xe^{x^2`

Explanation:

Properties of derivative :

1)
`(d)/(dx)(e^x)=e^x`

2)
`(d)/(dx)(x^n)=x^(n-1)`

3)
`(d)/(dx)(ax)=a`

Let g be a differentiable function , then

4)
`(d)/(dx)e^g=e^g(dg)/(dx)`

Given function :
`y = 4e^(x^2)`

Differentiate both sides with respect to x , we get

`y'=4e^(x^2)(d(x^2))/(dx)` (By (4))

`\Rightarrow\ y'=4e^(x^2)(2x)` (By (2))

`\Rightarrow\ y'=8xe^(x^2)`

Hence, the derivative of the given function is
`8xe^{x^2` .