What is the derivative of? : $(x^2+2)e^(4x)$

Question

(Question Restore: portions of this question have been edited or deleted!)

1421 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-15T16:40:59

(D) is an intermediate step.

$dy/dx = 2(2x^2+x+4)e^(4x)$

We will apply the Product Rule for Differentiation:

$d/dx(uv)=u(dv)/dx+(du)/dxv$ , or, $(uv)' = (du)v + u(dv)$

So with $y = (x^2+2)e^(4x)$ ;

${ ("Let", u = x^2+2, => (du)/dx = 2x), ("And" ,v = e^(4x), =>(dv)/dx = 4e^(4x) ) :}$

Then:

$d/dx(uv)=u(dv)/dx + (du)/dxv$

Giving:

$dy/dx = (x^2+2)(4e^(4x)) + (2x)(e^(4x))$
$\ \ \ \ \ \ = 2(2x^2+x+4)e^(4x)$