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

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

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

##### 1 Answer

Jan 15, 2018

(D) is an intermediate step.

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

#### Explanation:

We will apply the Product Rule for Differentiation:

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

So with

# { ("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) #