Derivative of e^2x(x^2-2)

Question

Finding the derivative of the function of e^2x(x^2-2).

Answer 1

Recall the formula

d/dx uv = udv/dx+vdu/dx

d/dx e^x = e^x

Given f(x) = e^2x(x^2-2) = x^2e^2x-2e^2x

 f(x)= x^2e^2x-2e^2x

Apply derivative to each sides with respect of x.

= d/dx( x^2e^2x-2e^2x)

= d/dx(x^2e^2x)-d/dx(2e^2x)

= x^2e^2x(2)+e^2x(2x)-2e^2x(2)

= 2x^2e^2x+2xe^2x-4e^2x

= 2e^2x(x^2+x-4)