If y =sin (sin (sin x )),then dy /dx =?

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lemjay | High School Teacher | (Level 2) Senior Educator

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`y=sin(sin(sinx))`

To solve for dy/dx, apply chain rule.

So, take the derivative of the outermost function first.

`(dy)/(dx)= [sin(sin(sinx))]'`

`(dy)/(dx)=cos (sin(sinx))*[sin(sinx)]'`

`(dy)/(dx)=cos (sin(sinx))*cos(sinx)*[sinx]'`

`(dy)/(dx)=cos (sin(sinx))*cos(sinx)*cosx*[x]'`

`(dy)/(dx)=cos (sin(sinx))*cos(sinx)*cosx*1`

`(dy)/(dx)=cos (sin(sinx))*cos(sinx)*cosx`

 

Hence,  `(dy)/(dx)=cosx*cos(sinx)*cos(sin(sinx))` .

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