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

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Answer 1 · 2016-02-18T00:04:01

If: g(x) = a(x)b(x)
then:
g'(x) = a'(x)b(x) + a(x)b'(x)
Hence for:
$g (x) = (2 x - 5) (x^{2} + 3)$ $g(x)=(2x - 5)(x^2 + 3)$
$g'(x) = 6x^2 - 10x +6$

If: g(x) = a(x)b(x)
then:
g'(x) = a'(x)b(x) + a(x)b'(x)

If: g(x) $=(2x - 5)(x^2 + 3)$
then: a= $(2x - 5)$ and $b=(x^2 + 3)$
Derivative of a = a'(x) = 2
Derivative of b = b'(x) = 2x

Thus:
$g'(x)=(2x-5)(2x)+(2)(x^2 + 3)$
$g'(x)=(4x^2 -10x) + (2x^2 + 6)$
$g'(x)=6x^2 - 10x +6$

How do you differentiate g(y) =(2x-5 )(x^2 + 3) g(y)=(2x−5)(x2+3)g(y) =(2x-5 )(x^2 + 3) using the product rule?