How do you find the derivative of #y=x^tan(x)#?
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.
The first step is to take the natural log of both sides:
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:
We know that the derivative of
Multiply both sides by
And there is the derivative.