Question

Derivative of x^(cos(x))

For the steps, I am a bit confused with how it is
cos(x)-xlog(x)sin(x), how is the cos(x) there?

Isn't the formula (a^x)(lna)?

Answer 1

you have a variable in the exponents so you need to take the log as the first step, or rewrite as \[x^{\cos(x)}=e^{\cos(x)\ln(x)}\] and use the chain rule

Answer 2

it is the same in either case, and all the work comes in finding the derivative of
\[\cos(x)\ln(x)\] using the product rule

Answer 3

from what you just told me to use product rule, i obtained
\[-\sin (x)(\ln x)-\cos (x)(1\div x)\]