How do you differentiate #f(x)= (2x^2-5)(4x^2+5) # using the product rule?
1 Answer
Dec 8, 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 ".
So with
# \ \ \ \ \ d/dx(uv) = u(dv)/dx + (du)/dxv #
# :. d/dx(uv) = (2x^2-5)(8x) + (4x)(4x^2+5) #
# :. d/dx(uv) = (4x){2(2x^2-5) + (4x^2+5)} #
# :. d/dx(uv) = (4x)(4x^2-10+4x^2+5) #
# :. d/dx(uv) = (4x)(8x^2-5) #