Question

Differentiation Question:

Answer 1

According to Wolfram Alpha the derivative of \[\sin ^x(x)\] is \[\sin ^x(x)(x \cot (x) + \ln (\sin (x)))\] but when I work it out I get \[\ln (\sin (x))+\cot (x)\ln (x)\] Could someone explain if how they're equal, if they are actually equal?

Answer 2

@Hero ?
@Preetha ?

Answer 3

they are not equal

Answer 4

\[\sin^x(x)=e^{x\ln(\sin(x))}\] take the derivative of that using the chain rule and the product rule

Answer 5

is that what you did, or did you "take the log"
you get the same answer either way, all the work is taking the derivative of \[x\ln(\sin(x))\]

Answer 6

@satellite73 Ok, thanks, I see my error now.