if y = (sin x)^x^2 then differentiate this!!!!! Pls give full steps!!!!!!

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if y = (sin x)^x^2 then differentiate this!!!!! Pls give full steps!!!!!!

Mathematics
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chane rule
use d f(x)^g(x)/ dx = f(x)^g(x)d/dx(g(x)log(f(x)) This can be proved easily
=cos x *2x

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so here i gotta apply the chain rule got it so i have to learn it keep answering ppl i will just go through and then maybe I will be able to understand the solution!!!!
keep posting what you do!
ok
@ruba: not you, I was telling that to tejeshwar so that he may understand and we may correct him if you are wrong
Tejeshwar: this is not exaclty chain rule, f(x)^g(x) is a bit different thing
nope sure its chain rule
First take y=sin(x)^x^2 log(y)=x^2log(sinx) d/dx on both sides so you get, 1/y dy/dx = d/dx (x^2log(sinx)) therefore, dy/dx=y d/dx(x^2log(sin(x))
\[sin(x)^{x^2}\]?
ohhhhhhh so so so s o sry mogh im jst 4geting this
if so take the log, simplify, take the derivative, then multiply by \[sin(x)^{x^2}\]
ri8 ri8 sat & mogh go on nd bye
Take this into consideration, y = f(x)^g(x) log y = g(x) log(f(x)) \[(1/y)dy/dx = d/dx(g(x)\log(f(x)))\]
\[ln(sin(x)^{x^2})=x^2ln(sin(x))\] \[\frac{d}{dx}x^2ln(sin(x))=2xln(sin(x))+\frac{x^2}{x}=2xln(sin(x))+x\] answer: \[(sin(x))^{x^2}(2xln(sin(x))+x)\]
oops sorry wrong
\[\frac{d}{dx}x^2ln(sin(x))=2xln(sin(x))+\frac{x^2}{sin(x)}\]
my mistake. sorry.
@satellite: d/dx ln(sin(x)) is \[cosx/sinx\]
wow am i off . you are right and i am wrong!
two mistakes in one post i should resign.
lol, it happens!
btw it is also correct two write \[(sin(x))^{x^2}=e^{x^2ln(sin(x))}\] and differentiate this using the chain rule. the actual work is identical since it all boils down to finding the derivative of \[x^2ln(sin(x))\]CORRECTLY
just hang on satellite i will just be back 1ce i understand the chain rule!!!!
Chain rule is easier than it looks, just check out the proof too! Regards.

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