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

1 Answer
Mar 19, 2016

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

Explanation:

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.