How do you differentiate #f(x)=sqrtsin(2-x^3) # using the chain rule?

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Answer 1 · 2016-03-19T12:30:54

#dy/dx=-1/2[sqrtsin(2-x^3)]cos(2-x^3)*3x^2#

Let #y=sqrtsin(2-x^3)#

Differentiating w.r.t. #x#

#dy/dx=d/dxsqrtsin(2-x^3)#

#dy/dx=1/2[sqrtsin(2-x^3)]*d/dxsin(2-x^3)#

#dy/dx=1/2[sqrtsin(2-x^3)]cos(2-x^3)*d/dx2-x^3#

#dy/dx=1/2[sqrtsin(2-x^3)]cos(2-x^3)*(-3x^2)#

#dy/dx=-1/2[sqrtsin(2-x^3)]cos(2-x^3)*3x^2#

This will be the differentiated function.