Use the product rule to find the derivative of (2x^2 + 3)(3x + 5).

Answer 1

recall that the derivative of f(x)*g(x) is just
f'(x)*g(x) + f(x)*g'(x)
which means, we first take the derivative of the first function of x (the f(x)) then multiply this by the second function of x (the g(x)) and add this to the product of f(x) and derivative of g(x).

from the problem,
let f(x) = (2x^2 + 3)
let g(x) = (3x + 5)
thus
f'(x) = 4x
g'(x) = 3
and therefore,
f'(x)*g(x) + f(x)*g'(x)
(4x)(3x+5) + (2x^2 + 3)(3)
12x^2 + 20x + 6x^2 + 9
18x^2 + 20x + 9

hope this helps~ :)

Answer 2

Duplicate post.

See also
http://www.jiskha.com/display.cgi?id=1303800740