Thursday, 7 November 2013

`y = sqrt(x + sqrt(x + sqrt(x)))` Find the derivative of the function.

`y=sqrt(x+sqrt(x+sqrt(x)))`


`y'=(1/(2sqrt(x+sqrt(x+sqrt(x))))) *d/dx (x+sqrt(x+sqrt(x)))`


`y'=(1/(2sqrt(x+sqrt(x+sqrt(x))))) *(1+d/dxsqrt(x+sqrt(x)))` 


`y'=(1/(2sqrt(x+sqrt(x+sqrt(x))))) *(1+(1/(2sqrt(x+sqrt(x)))*d/dx
(x+sqrt(x))))`

`y'=(1/(2sqrt(x+sqrt(x+sqrt(x)))))
*(1+(1/(2sqrt(x+sqrt(x))))*(1+d/dxsqrt(x)))`


`y'=(1/(2sqrt(x+sqrt(x+sqrt(x))))) *(1+(1/(2sqrt(x+sqrt(x)))) *(1+1/(2sqrt(x))))`

`y'=(1/(2sqrt(x+sqrt(x+sqrt(x))))) *(1+(1/(2sqrt(x+sqrt(x))))
*((2sqrt(x)+1)/(2sqrt(x))))`

`y'=(1/(2sqrt(x+sqrt(x+sqrt(x)))))
*(1+(2sqrt(x)+1)/(4sqrt(x)sqrt(x+sqrt(x))))`


`y'=(1/(2sqrt(x+sqrt(x+sqrt(x)))))
*((4sqrt(x)sqrt(x+sqrt(x))+2sqrt(x)+1)/(4sqrt(x)sqrt(x+sqrt(x))))`


`y'=(4sqrt(x)sqrt(x+sqrt(x))+2sqrt(x)+1)/(8sqrt(x)sqrt(x+sqrt(x))sqrt(x+sqrt(x+sqrt(x))))`

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