Question

Find the derivative of function y = 4sin x /(3-5 sin x)

Which one is my u', u, v' and v? I'm trying to use the d(u/v) u'v - v'u /(v)^2 formula.

Answer 1

So it looks like you have \[y=\frac{ 4sinx }{ 3-5sinx }\] correct?

Answer 2

Yes.

Answer 3

Perfect. So here is what we first do. We recognize that we have a quotient (a fraction), something over something else. So we use the quotient rule to take the derivative.

Answer 4

So our numerator can be our u, and our denominator can be v
So u=4sinx and v=3-5sinx
so what is u' and what is v', well take the derivative of each. Can you do that?

Answer 5

for example if u=3cosx then u'=-3sinx

Answer 6

ah okay so u'= 4 cos x and v' = 3+4 cosx?

Answer 7

so your u' is correct, but remember if v=3-5sinx we have
v'= 3'-(5sinx)'=0-5cosx=-5cosx

Answer 8

does that make sense? because we take the derivative of each term of v, and we must remember that the derivative of a number is simply 0

Answer 9

Yes, that clarifies my confusion. Thank you so much!

Answer 10

so now you plug it in :-) The quotient rule simply states in words
(derivative of the top)*(bottom)-(top)*(derivative of bottom) all divided by the bottom squared

Answer 11

You are welcome!