# How do you differentiate #f(x)=1/(x^sqrt(x-3))# using the chain rule?

##### 1 Answer

#### Explanation:

So we have

Taking the log of both sides we have

Derivating we have

Using the chain rule on the left hand side we have

Isolating

It's important to notice we can't simply say

Because that only works for constant values on the exponent! Nor can we say

Because that only works when the base is a constant! If both base and exponent change, you need to use implicit differentiation with logs.