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))

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- Aug 22nd 2010, 05:52 AMjasonlewizderivatives of trigo identity
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)) - Aug 22nd 2010, 06:09 AMArchie Meade
- Aug 22nd 2010, 03:45 PMArchie Meade
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...

$\displaystyle \displaystyle\frac{dt}{dx}=\frac{dt}{dw}\ \frac{dw}{dv}\ \frac{dv}{du}\ \frac{du}{dx}$

$\displaystyle =\displaystyle\frac{d}{dw}w^2\ \frac{d}{dv}Sinv\ \frac{d}{du}Sinu\ \frac{d}{dx}Sinx$

$\displaystyle =[2w][Cosv][Cosu][Cosx]=[2Sinv][Cos(Sinu)][Cos(Sinx)][Cosx]$

$\displaystyle =[2Sin(Sinu)][Cos(Sin(Sinx))][Cos(Sinx)][Cosx]$

$\displaystyle =[2Sin(Sin(Sinx))][Cos(Sin(Sinx))][Cos(Sinx)][Cosx]$ - Aug 24th 2010, 02:15 AMtom@ballooncalculus
Just in case a picture helps...

http://www.ballooncalculus.org/draw/diffChain/nest.png

... where (key in spoiler) ...

__Spoiler__:

__Spoiler__:

Alternatively...

http://www.ballooncalculus.org/draw/diffChain/nestb.png

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