Question

Derivative of:

(sin(x))^(sin(x)) ??

Answer 1

\[\sin(x)^{sinx-1} * \cos (x)\]

Answer 2

)??? I don't know if this is right,, looks strange.

Answer 3

cos(x)sin(x)[sin(x)]^[sin(x)-1] sorry mistyped it before

Answer 4

this problem actually stumped me and when in doubt use wolfram alpha http://www3.wolframalpha.com/Calculate/MSP/MSP297019g94542i91011ia00000e4a3b80hc49a9be?MSPStoreType=image/gif&s=25&w=491&h=364

Answer 5

in wolfram its showing for sin^(sinx) (x)

Answer 6

Lol, I did too, but it kept rewriting my equation...Is it still correct the way that Wolfram rewrites it?

Answer 7

my ti-89 says something else...

Answer 8

yah when you deal with trig functions like that they can be written as sin^2(x) = (sin(x))^2

Answer 9

it gave cos(x) ln(sinx) + cos(x)*sin(x)^sin(x)

Answer 10

That looks good to me. Thank you ALL OF YOU for your time and effort!

Answer 11

you're very welcome ramos

Answer 12

lol what

Answer 13

y= sinx ^ sinx

take log both sides

ln(y) = ln [ sinx ^ sinx ]

ln(y) = sin(x) ln (sin(x))

Answer 14

(1/y) dy/dx = sin(x) [ cot(x)] + cos(x)ln(sin(x) )

Answer 15

\[\frac{dy}{dx} = [ \sin(x)]^{\sin(x)} [ \sin(x)\cot(x) + \cos(x)\ln(\sin(x)) ]\]