How do you differentiate $f(x)=(5-x^2)(x^3-3x+3)$ using the product rule?

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Answer 1 · 2015-12-27T00:18:40

$f'(x) = -5x^4 +24x^2 -6x-15$

Derivative of product rule

Given $" " " h= f*g$

$h' = fg' +f'g$

The original problem

$f(x) = (5-x^2)(x^3-3x+3)$

$f'(x) = (5-x^2) d/dx(x^3-3x+3) + d/dx(5-x^2)(x^3-3x+3)$

$=> (5-x^2)(3x^2-3) + (-2x)(x^3-3x+3)$

Now we can multiply and combine like terms

$=> (15x^2 -15 -3x^4 +3x^2) +( -2x^4+6x^2 -6x)$
$=> -5x^4 +24x^2 -6x-15$

How do you differentiate f(x)=(5-x^2)(x^3-3x+3) f(x)=(5-x^2)(x^3-3x+3) using the product rule?