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