Differentiating Exponentials and Logarithms

You will need to know how to differentiate expressions containing exponentials and logarithms. These are the standard results of the cases you need to know:

What is the derivative of lnkx ?

It is the same as the standard result of lnx. But why? As lnkx is equal to lnx + lnk where lnk is a constant, after the expression of lnkx is differentiated, lnk disappears leaving the standard result of lnx.

The standard result of e^kx can be used to prove the standard result of a^kx:

Example 1:

Note: This can also be proved by implicit differentiation. See the implicit differentiation guide for that proof.

Example 2:

Practice Question:

Show Answer