Question

What is the derivative of `2^x`?

Answer 1

Derivative of `2^x` is `2^xln2`

Explanation:

Let `y=2^x`. Now to find `(dy)/(dx)`, let us take logarithm on both sides, which gives

`lny=xln2` - now taking implicit differential on both sides

`1/y(dy)/(dx)=ln2`

and hence`(dy)/(dx)=yln2=2^xln2`