Answer: The derivative would be [tex]y'=12x^2e^{-x}-4x^3e^{-x}[/tex]
Step-by-step explanation:
Since we have given that
[tex]y=4x^3e^{-x}[/tex]
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
[tex]\dfrac{d}{dx}x^3=3x^2\\\\and\\\\\dfrac{d}{dx}e^{-x}=-e^{-x}[/tex]
Now, we will get that
[tex]y'=(4x^3)'e^{-x}+(4x^3)\times (e^{-x})'\\\\y'=12x^2e^{-x}-4x^3e^{-x}[/tex]
Hence, the derivative would be [tex]y'=12x^2e^{-x}-4x^3e^{-x}[/tex]
