How do you differentiate f(x)=(x^3-4)(x^2-3)f(x)=(x34)(x23) using the product rule?

1 Answer
Apr 23, 2018

3x^2(x^2-3) + "2x(x^3-4)3x2(x23)+2x(x34)

Explanation:

when two distinct functions are multiplied together:

f(xy) = (x^3-4)(x^2-3)f(xy)=(x34)(x23)

We can use the product rule to work out the differential:

f'(xy) = f(x) * f'(y) + f(y) * f'(x)

f(x) = (x^3−4)
f'(x) = 3x^2

f(y) = (x^2-3)
f'(y) = 2x

Can also be written as (uv)' = uv' + vu'
u = (x^3−4)
u' = 3x^2
v = (x^2-3)
v' = 2x