Question

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

f(x) = x2 + 1)e4x

Answer 1

f'(x)
`=2(e^4^x)+(x^2+1)(4e^4^x)`

Explanation:

The derivative of the function:

`(x^2+1)e^4^x`

The rule for the product of two functions:

f'(x)
`=g'(x)h(x)+g(x)h'(x)`

Therefore

g(x)
`=x^2+1`

g'(x)
`=2`

f(x)
`=e^4^x`

f'(x)
`=4e^4^x`

f'(x)
`=2(e^4^x)+(x^2+1)(4e^4^x)`