# How do you find the derivative of # y = sin(x cos x)# using the chain rule?

##### 1 Answer

#### Explanation:

You will need to use the product rule to find

**Use of the Product Rule**

If you are studying maths, then you should learn the Product Rule for Differentiation, and practice how to use it:

# d/dx(uv)=u(dv)/dx+v(du)/dx # , or,# (uv)' = (du)v + u(dv) #

I was taught to remember the rule in words; "*The first times the derivative of the second plus the second times the derivative of the first* ".

So with

# d/dx(xcosx) =(x)(d/dxcosx) + (cosx)(d/dxx) #

# :. d/dx(xcosx) = (x)(-sinx) + (cosx)(1) #

# :. d/dx(xcosx) = cosx-xsinx # .... [1]

**Use of the Chain Rule**

You should learn the Chain Rule for Differentiation, and practice how to use it:

If

# y=f(x) # then# f'(x)=dy/dx=dy/(du)(du)/dx #

I was taught to remember that the differential can be treated like a fraction and that the "

# dy/dx = dy/(dv)(dv)/(du)(du)/dx # etc, or# (dy/dx = dy/color(red)cancel(dv)color(red)cancel(dv)/color(blue)cancel(du)color(blue)cancel(du)/dx) #

So, If

Using

# dy/dx=(cosu)(cosx-xsinx) #

# :. dy/dx=(cosx-xsinx)*cos(xcosx) #