## anonymous 4 years ago Find the derivative of the trigonometric function. y=2xsinx+x^2cosx

$y'=\frac{d}{dx}(2xsinx)+ \frac{d}{dx}x^2cosx$

2. cwrw238

use product rule

3. anonymous

product rule for addition?

use product rule for each term

5. anonymous

ah ok

6. cwrw238

no - apply product rule to each of the two terms - looks like diyad is doing that now

First do $$\frac{d}{dx}(2xsinx)$$ & then $$\frac{d}{dx}(x^2cosx)$$

do you know how to do derivative of 2xsinx ?

9. cwrw238

d (uv)dx = u* dv/dx + v* du/dx where u and v are function of x

10. anonymous

so

11. anonymous

2xsix+x^2cosx=2sinx+3xcosx+2xcosx-x^2sinx

12. anonymous

2sinx oops

Nope

14. anonymous

2xsinx

15. anonymous

4xcosx+2sinx-x^2sinx

16. anonymous

4xcosx+sinx(2-x^2)

17. anonymous

i mistyped a bunch at first lol

$\frac{d}{dx} (2xsinx)= 2 \frac{d}{dx}(xsinx) =2[x \frac{d}{dx}sinx+sinx \frac{d}{dx}x]$

19. anonymous

my last answer is correct

20. anonymous

4xcosx+sinx(2-x^2)

21. anonymous

atleast thats what the books says in the back.

$\frac{d}{dx}(2xsinx)=2[xcosx+sinx]$

23. anonymous

y=2xsinx+x^2cosx = 2sinx+2xcosx+2xcosx-x^2sinx = 4xcosx +2sinx - x^2sinx = 4xcosx + sinx(2-x^2)

24. cwrw238

thats correct ChrisV

25. anonymous

thanks guys

oh sorry i thought you were taling about the derivative of 2xsinx

27. anonymous

did not know i could use product rule on both sides

28. anonymous

better to learn than wonder :)

29. cwrw238

yep - whenever you have a product of two functions the rule applies