Question

how find the derivative of f(x)=sin(x)^x ?!

Answer 1

\[ f(x)=\sin(x)^x \]

Answer 2

\[x \epsilon (0,\pi)\]

Answer 3

start by taking log on both sides
log f(x) =.....

Answer 4

Please ln both sides

Answer 5

you should get lnf(x)=xln(sinx)

Answer 6

y= sinx^x as
hartnn said take log for both
log y= x log x
nw deff both side for x , then but insted of y ,sinx ^x

Answer 7

f(x)=e^(xln(sinx))

Answer 8

use e's derivative and you should get an answer for dy/dx

Answer 9

is the answer is like this @shakesworde

Answer 10

YES, thats correct
that can also be simplified one step further, if required.

Answer 11

how ?! to simplify @hartnn ?!

Answer 12

for one thing, cos x/ sin x = cot x

but the 1st term,
e^(xln sin x ) can be simplified using the fact that e^ln A = A
as
sin x^x

Answer 13

i see, thanks @ hartnn

Answer 14

welcome ^_^