Question

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

y = 4x3e - x

Answer 1

Answer: The derivative would be
`y'=12x^2e^(-x)-4x^3e^(-x)`

Explanation:

Since we have given that

`y=4x^3e^(-x)`

We need to find the derivative of the function:

We will use "Product rule"

f'(x)= derivative of first function × second function + derivative of second function × first function.

As we know that

`(d)/(dx)x^3=3x^2\\\\and\\\\(d)/(dx)e^(-x)=-e^(-x)`

Now, we will get that

`y'=(4x^3)'e^(-x)+(4x^3)* (e^(-x))'\\\\y'=12x^2e^(-x)-4x^3e^(-x)`

Hence, the derivative would be
`y'=12x^2e^(-x)-4x^3e^(-x)`