Question

What is the derivative of `2^x`?

Answer 1

`2^xln2`

Explanation:

let `y=2^x`

Take ln ( natural log) of both sides.

`rArrlny=ln2^x=xln2`

differentiate `color(blue)"implicitly with respect to x"`

`rArr1/y.dy/dx=ln2`

`rArrdy/dx=yln2=2^xln2`