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

##### 1 Answer

Jul 8, 2017

#### Answer:

# f'(x) = -2(2x-3)^2(5x^2+3x-12) #

#### Explanation:

We have:

# f(x )= (4-x^2)(2x-3)^3 #

So using the product rule we have:

# f'(x )= {4-x^2}{ d/dx (2x-3)^3} + {d/dx (4-x^2)}{(2x-3)^3} #

So using the chain rule we have:

# f'(x) = {4-x^2}{ 3(2x-3)^2(2)} + {-2x}{(2x-3)^3} #

# " " = 6(4-x^2)(2x-3)^2 -2x(2x-3)^3 #

# " " = 2(2x-3)^2{3(4-x^2) -x(2x-3)} #

# " " = 2(2x-3)^2(12-3x^2 -2x^2+3x) #

# " " = 2(2x-3)^2(-12-5x^2-3x) #

# " " = -2(2x-3)^2(5x^2+3x-12) #