I don't how to start with this kind of problem. Can someone show me the solution for this one.
Find the first derivative
sin^2(sin(sin x))
If you like you can write....
$\displaystyle u=Sinx$
$\displaystyle v=Sinu$
$\displaystyle w=Sinv$
$\displaystyle t=w^2$
then, using the Chain Rule of differentiation...
$\displaystyle \displaystyle\frac{dt}{dx}=\frac{dt}{dw}\ \frac{dw}{dv}\ \frac{dv}{du}\ \frac{du}{dx}$
$\displaystyle =\displaystyle\frac{d}{dw}w^2\ \frac{d}{dv}Sinv\ \frac{d}{du}Sinu\ \frac{d}{dx}Sinx$
$\displaystyle =[2w][Cosv][Cosu][Cosx]=[2Sinv][Cos(Sinu)][Cos(Sinx)][Cosx]$
$\displaystyle =[2Sin(Sinu)][Cos(Sin(Sinx))][Cos(Sinx)][Cosx]$
$\displaystyle =[2Sin(Sin(Sinx))][Cos(Sin(Sinx))][Cos(Sinx)][Cosx]$
Just in case a picture helps...
... where (key in spoiler) ...
Spoiler:
Spoiler:
Alternatively...
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Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
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