Question

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

Answer 1

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

Explanation:

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`