Question

derivatives of exponents

Answer 1

y=x^sinx

Answer 2

I got \[\frac{ dy }{ dx }=x ^{sinx}*lnx\]

Answer 3

but I am not confident with that

Answer 4

one easy way to do this is to take the log. d/dx ln(y(x)) = y'/y.
d/dx ln(x^sin(x))=d/dx (sin(x) ln(x))=y'/(x^(sin(x)). solve for y'.

Answer 5

the answer is x^(sin(x))*(cos(x)ln(x)-sin(x)/x)