Question

How do you differentiate `f(x)= (3x+1)^4(4-x^2)` using the product rule?

Answer 1

`dy/dx=[-2x(3x+1)^4]+[(48-12x^2)(3x+1)^3]`

Explanation:

Given -

`f(x)=(3x+1)^4(4-x^2)`
`y=(3x+1)^4(4-x^2)`

Use chain rule and product rule to differentiate this -

`dy/dx=[(3x+1)^4(-2x)]+[(4-x^2)(4)(3x+1)^3(3)`
`dy/dx=[-2x(3x+1)^4]+[12(4-x^2)(3x+1)^3]`
`dy/dx=[-2x(3x+1)^4]+[(48-12x^2)(3x+1)^3]`