Question

differentiate the function...

Answer 1

\[y=(sinx)^{lnx}\]

Answer 2

you have a choice
you can either write
\[\large \sin(x)^{\ln(x)}=e^{\ln(x)\ln(\sin(x))}\] and use the chain rule, or you can take the log, get
\[\ln(x)\ln(\sin(x))\] find the derivative, and then multiply by the original function
all the work is essentially the same, finding the derivative of
\[\ln(x)\ln(\sin(x))\] using product rule and chain rule

Answer 3

would the answer be this (ln(sin(x))/x + ln(x)cot(x))(sin(x))^ln(x)

Answer 4

yes, i think that looks good