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

Apr 23, 2018

3x^2(x^2-3) + "2x(x^3-4)

Explanation:

when two distinct functions are multiplied together:

$f \left(x y\right) = \left({x}^{3} - 4\right) \left({x}^{2} - 3\right)$

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

$f ' \left(x y\right) = f \left(x\right) \cdot f ' \left(y\right) + f \left(y\right) \cdot f ' \left(x\right)$

 f(x) = (x^3−4)
$f ' \left(x\right) = 3 {x}^{2}$

$f \left(y\right) = \left({x}^{2} - 3\right)$
$f ' \left(y\right) = 2 x$

Can also be written as $\left(u v\right) ' = u v ' + v u '$
 u = (x^3−4)
$u ' = 3 {x}^{2}$
$v = \left({x}^{2} - 3\right)$
$v ' = 2 x$