Derivative proof:

y=a^x

Take the logarithm of both sides at the same time and get: lny=xlna.

Derive x on both sides at the same time and get: y'/y=lna.

So y' = ylna = a xlna proves this point.

Extended data

Matters needing attention

1. Not all functions can be exported;

2. The derivable function must be continuous, but the continuous function is not necessarily derivable (for example, y=|x| is not derivable at y=0).

Partial derivative formula:

1.y=c(c is a constant) y'=0

2.y=x^n y'=nx^(n- 1)

3.y=a^x； y'=a^xlna； y=e^x y'=e^x

4 . y = logax y ' = logae/x； y=lnx y'= 1/x

5.y=sinx y'=cosx

6.y=cosx y'=-sinx

7.y = Tanks Y' =1/cos 2x

8.y=cotx y'=- 1/sin^2x

9 . y = arcsinx y'= 1/√ 1-x^2

10 . y = arc cosx y'=- 1/√ 1-x^2

1 1 . y = arctanx y'= 1/ 1+x^2

12 . y = arccotx y'=- 1/ 1+x^2