# How do you differentiate #y=x^2lnx#?

##### 1 Answer

Nov 22, 2016

#### Explanation:

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+(du)/dxv # , 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 derivative of the first times the second* ".

This can be extended to three products:

# d/dx(uvw)=uv(dw)/dx+u(dv)/dxw + (du)/dxvw#

So with

# d/dx(uv)=u(dv)/dx + (du)/dxv #

# d/dx(x^2lnx)=(x^2)(1/x) + (2x)(lnx) #

# d/dx(x^2lnx)=x + 2xlnx #