## anonymous 5 years ago Find the first derivative of f(θ)=(θ+1)cosθ

1. amistre64

replace that theta thing with a normal looking variable for starters :)

2. amistre64

(x+1)cos(x) distribute the cos thru x cos(x) + cos(x) now derive both of them seperately

3. amistre64

Dx(x cosx) + Dx(cosx)

4. amistre64

the first term is a product, so use the product rule on it...

5. amistre64

x Dx(cosx) + Dx(x) cosx + Dx(cosx)

6. amistre64

-x sin(x) + cos(x) - sin(x)

7. nowhereman

That looks rather complicated. I would do it like this: $Df = \cos θ D(θ+1) + (θ+1)D\cos θ = \cos θ - (θ+1)\sin θ$

8. anonymous

9. nowhereman

Yes, and they yield the same result after all.

10. amistre64

Both answers are exactly the same :) I just didnt factor mine out.

11. anonymous

oh well thank you so much :)