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

1 Answer
Mar 19, 2016

Answer:

#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.