Question

How do you find the derivative of (cos x)^x?

Answer 1

Do you know how to find the derivative of x^x ?

Answer 2

no :(

Answer 3

Write y = x^x, then
ln y = x ln x

We can differentiate the left hand side, LHS, using the chain rule:
\[ y' \frac{1}{y} \]
the the derivative of the RHS is
\[ x.(1/x) + 1.\ln x = 1 + \ln x \]

Hence
\[ y' \frac{1}{y} = 1 + \ln x \]
and
\[ y' = y(1 + \ln x) = x^x(1 + \ln x) \]

Now, imitate that procedure for your problem.

Answer 4

Logarithmic differentiation.

Answer 5

Ok. Thanks! :)