Finding the derivative of: $ y(x)=x⋅\sin(x)+x^2⋅\cos(3x) $

Question

I am a student and I have a problem in solving this derivative, so please help me.
The problem: $$ y(x)=x⋅\sin(x)+x^2⋅\cos(3x)$$ I give this problem to online derivative calculator like derivative-calculator.net but the answer is not equal to my teacher answer.

online calc answer: $$ y^\prime(x)=−3x2⋅\sin(3x)+2x⋅\cos(3x)+\sin(x)+x⋅\cos(x) $$ teacher answer: $$ y^\prime(x) = 1⋅\sin(x)+x⋅\cos(x)+2x⋅\cos(3x)-3x^2⋅\sin(3x) $$ what is the correct answer? thanks.

How will you do this problem if the all online derivative calculators suddenly disappear ? — Claude Leibovici, Dec 31 '13 at 10:52
No this question should not be closed as "unclear what you're asking". — Eric Stucky, Jan 06 '14 at 04:21

score 1 · Accepted Answer · answered Dec 31 '13 at 10:17

1

The two are the same in different order since the first term of the first equation should be $$-3x^2\cdot \sin(3x).$$

answered Dec 31 '13 at 10:17

mathlove

139,939

score 0 · Answer 2 · 2013-12-31T10:23:30.853

0

Both answers are actually correct. In fact, they are the same. For future reference use this online software:http://www.wolframalpha.com/input/?i=find+the+derivative+of+x%E2%8B%85sin%28x%29%2Bx%5E2%E2%8B%85cos%283x%29. But I hope you know how to use the product rule.

edited Dec 31 '13 at 10:23

answered Dec 31 '13 at 10:18

Finding the derivative of: $ y(x)=x⋅\sin(x)+x^2⋅\cos(3x) $

2 Answers2