# How do you find the derivative of #y=x^nlnx#?

##### 1 Answer

Dec 19, 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

Applying the product rule we get:

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

# :. d/dx(x^nlnx)=(x^n)(1/x) + (nx^(n-1))(lnx) #

# :. d/dx(x^nlnx)=x^(n-1) + nx^(n-1)lnx #