1. ## differentiation

This is the problem

If g(x) = (ax^2 + bx + c) sinx + (dx^2 + ex + f) cos x

determine the values of the constants a, b, c,d,e, f

such that g'(x) = x^2 sinx

2. Originally Posted by ClipsClips99
This is the problem

If g(x) = (ax^2 + bx + c) sinx + (dx^2 + ex + f) cos x

determine the values of the constants a, b, c,d,e, f

such that g'(x) = x^2 sinx
$g \prime (x) = (2ax + b)sin(x) + (ax^2 + bx + c)cos(x) + (2dx + e)cos(x) - (dx^2 + ex + f)sin(x)$

$= (-dx^2 + [2a - e]x + [b - f])sin(x) + (ax^2 + [b + 2d]x + [c + e])cos(x)$

$= x^2 sin(x)$

So by matching up the coefficients I get
-d = 1
2a - e = 0
b - f = 0
a = 0
b + 2d = 0
c + e = 0

This gives me the solution:
a = 0
b = 2
c = 0
d = -1
e = 0
f = 2

-Dan