Question

Find the first derivative of f(θ)=(θ+1)cosθ

Answer 1

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

Answer 2

(x+1)cos(x) distribute the cos thru

x cos(x) + cos(x) now derive both of them seperately

Answer 3

Dx(x cosx) + Dx(cosx)

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

could both answers be used as the correct answer?

Answer 9

Yes, and they yield the same result after all.

Answer 10

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

Answer 11

oh well thank you so much :)