# How do you find the derivative of #y=x^tan(x)#?

##### 1 Answer

This is a type of problem involving logarithmic differentiation.

Whenever you're trying to differentiate a variable raised to some power also involving that variable, it's a good hint that logarithmic differentiation will help you out.

1.)

The first step is to take the natural log of both sides:

2.)

Using the exponents property of logarithms, we bring the exponent out in front of the log as a multiplier. This is done to make differentiating easier:

3.)

Now we implicitly differentiate, taking care to use the chain rule on

4.)

We know that the derivative of

5.)

Multiply both sides by

6.)

We know

7.)

And there is the derivative.