How do you find the derivative of x+2^x?

1 Answer
Sep 11, 2017

1+2^xln2

Explanation:

because differentiation is a linear operator we have:

d/(dx)(x+2^x)=d/(dx)(x)+d/(dx)(2^X)
=1+d/(dx)(2^x)---(1)

let us do the second differentiation separately.

let y=2^x

=>lny=ln(2^x)=xln2

d/(dx)(lny)=d/(dx)(xln2)

1/ydy/(dx)=ln2

dy/(dx)=yln2=2^xln2

:." "(1)" becomes "1+2^xln2