Differentiate the following function u = Cos(x3)

 u = Cos(x³)

To differentiate this function we will use the chain rule. Firstly we will set x³  to another variable name such as v. So now v = x³ . Lets differentiate this. dv/dx = 3x²

We can now differentiate cos(v) du/dv = -sin(v). Now to complete the chain rule we must do dv/dx*du/dv. Which will be -sin(v)*3x²  = -3x²sin(v). Now we can just put the x³ back in instead of the v and our final answer will be -3x²sin( x³).