`y = (x + (x + sin^2(x))^3)^4` Find the derivative of the function.

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hkj1385 eNotes educator| Certified Educator

Note:- 1) If y = x^n ; then dy/dx = n*{x^(n-1)}

2) If y = sin(x) ; then dy/dx = cos(x)

3) If a function to be differentiated contains sub-functions,then by the rule of differentiation, the last function is differentiated first.

4) 2sinx*cosx = sin(2x)

Now, for the given question , find the solution in the attachment

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gsarora17 eNotes educator| Certified Educator

`y=(x+(x+sin^2x)^3)^4`

`y'=4(x+(x+sin^2x)^3)^(4-1)*((1+3(x+sin^2x)^(3-1)*(1+2sinxcosx))`

`y'=4(x+(x+sin^2x)^3)^3 *((1+3(x+sin^2x)^2 *(1+sin2x))`