How do you differentiate g(x) = xe^(2x)g(x)=xe2x using the product rule?

1 Answer
Aug 22, 2016

The result is (2x+1)e^(2x).

Explanation:

The rule says that d/dx f(x)*g(x)=df(x)/dx*g(x)+f(x)*dg(x)/dxddxf(x)g(x)=df(x)dxg(x)+f(x)dg(x)dx.
In this case the two functions are xx and e^(2x)e2x.
Unfortunately the text call the product g(x)g(x) and this can create some confusion with my description of the product rule.

(dxe^(2x))/dx = dx/dx *e^(2x)+x*d/dxe^(2x)dxe2xdx=dxdxe2x+xddxe2x

=e^(2x)+x*2*(e^2x)=e2x+x2(e2x)

=(2x+1)e^(2x)=(2x+1)e2x.