What is the derivative of #x^(cosx)#?

1 Answer
Jul 29, 2015

Answer:

We shall attack this problem by logarithmic differentiation.

Explanation:

Let, #y = x^(cos x)#

Taking natural logarithm on both the sides, we obtain

# Ln y = Cos x Ln x#

Now, differentiating with respect to #x#,

#1/y(dy)/dx = Cos x/x - Sin xLn x#

In the last step, I used chain rule on the LHS and the product rule on the RHS.

Thus, #(dy)/dx = x^Cos x [Cos x/x - Sin xLn x]#