Question

Calculate dy/dx when y = (x2 + 2)e 4x as the derivative of a product, letting u = x2 + 2 and v = e4x . Which of the following is a step in your solution?

A. dv/dx = 4xe3x
B. du/dx = 2x + 2
C. dv/dx = 4xe4x
D. du/dx = 2x

Answer 1

D. du/dx = 2x

Explanation:

Given to find dy/dx where;

`y=(x^(2) +2)e^4^x`

Then when you let;

u=x²+2 and

`v=e^(4x)`

Then

In u=x²+2 du/dx = 2x------------------------step 1

In e^4x, dv/dx = e^4x * d/dx (4x)

=e^4x *4 = 4e^4x------------------------------------step 2