How do you differentiate f(x)=(e^x-3lnx)(tanx+2x)f(x)=(ex−3lnx)(tanx+2x) using the product rule?
1 Answer
Jan 5, 2016
Explanation:
The product rule states that for a function
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)