Question

Find the derivative:

y=x^(sin(x))

Answer 1

y = x^sinx

take ln of both sides
ln y = ln (x^sinx)
ln y = (lnx)(sinx)
y' / y = lnx(cosx) + (1/x)sinx

y' = y(lnx(cosx) + (1/x)sinx)
= (x^sinx)(lnx(cosx) + (1/x)sinx)