How do you differentiate #f(x)=x^3lnx # using the product rule?
1 Answer
Dec 12, 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^3lnx)=(x^3)(1/x) + (3x^2)(lnx) #
# :. d/dx(x^3lnx)=x^2 + 3x^2lnx #