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

##### 1 Answer

Mar 9, 2016

#### Answer:

#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]#