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

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Answer 1 · 2018-04-23T19:47:12

$3 x^{2} (x^{2} - 3) + 2 x (x^{3} - 4)$ $3x^2(x^2-3) + "2x(x^3-4)$

when two distinct functions are multiplied together:

$f (x y) = (x^{3} - 4) (x^{2} - 3)$ $f(xy) = (x^3-4)(x^2-3)$

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 $(uv)' = uv' + vu'$
$u = (x^3−4)$
$u' = 3x^2$
$v = (x^2-3)$
$v' = 2x$

How do you differentiate f(x)=(x^3-4)(x^2-3)f(x)=(x3−4)(x2−3)f(x)=(x^3-4)(x^2-3) using the product rule?