Product rule - -- -

Question

Answer 1

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

f'(x) = (x+2)(4x) + (2x^2 -3)

= 4x^2 +8x + 2x^2 -3

= 6x^2 +8x -3

product rule is

the derivative of two factors is

the (1st factor times the derivative of th 2nd) Plus the (2nd factor times derivative of the 1st factor)

derivative of the 2nd = 4x

derivative of the 1st = 1

or you could have multiplied the two factors together

and gotten f(x) = (x+2)(2x^2 -3) = 2x^3 +4x^2 -3x -6

then take the derivative to get

6x^2 +8x -3

that doesn't involve the "product rule" but if you're unsure what to do, that's a good way to check your answer.

work a problem 2 different ways, and if you get the same answer that's a good clue you did it correctly