Question

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

Answer 1

Answer: The derivative would be $y'=12x^2e^{-x}-4x^3e^{-x}$

Step-by-step 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

$\dfrac{d}{dx}x^3=3x^2\\\\and\\\\\dfrac{d}{dx}e^{-x}=-e^{-x}$

Now, we will get that

$y'=(4x^3)'e^{-x}+(4x^3)\times (e^{-x})'\\\\y'=12x^2e^{-x}-4x^3e^{-x}$

Hence, the derivative would be $y'=12x^2e^{-x}-4x^3e^{-x}$