How do you differentiate f(x)=(e^x-3lnx)(tanx+2x)f(x)=(ex3lnx)(tanx+2x) using the product rule?

1 Answer
Jan 5, 2016

f'(x)=(e^x-3/x)(tanx+2x)+(e^x-3lnx)(sec^2x+2)

Explanation:

The product rule states that for a function f(x)=g(x)h(x),

f'(x)=g'(x)h(x)+h'(x)g(x)

Thus

f'(x)=(tanx+2x)d/dx(e^x-3lnx)+(e^x-3lnx)d/dx(tanx+2x)

Find the derivative of each part separately.

d/dx(e^x-3lnx)=e^x-3/x

d/dx(tanx+2x)=sec^2x+2

Hence

f'(x)=(e^x-3/x)(tanx+2x)+(e^x-3lnx)(sec^2x+2)