# How do you differentiate #f(x)= (2x^2-5)(4x^2+5) # using the product rule?

##### 1 Answer

Dec 8, 2016

#### Answer:

#### 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) #