Question

find dy/dx for y = 3cos(x) + csc(x)

Answer 1

Do you know your derivative rules for trig functions? If not, you can find some here:
http://www.sosmath.com/calculus/diff/der03/der03.html

Answer 2

Heere is also a list of basic rules. This is a simple example where you have two functons added together. http://tutorial.math.lamar.edu/pdf/Common_Derivatives_Integrals.pdf

Answer 3

okay so do i just ignore the fact that its dy/dx because the y is already isolated?

Answer 4

Can you tell me what \[\Large \frac{ dy }{ dx } 3\cos(x)= ?\]

Answer 5

-3sin(x)

Answer 6

Ok and what is \[\Large \frac{dy}{dx} \csc(x)? \]

Answer 7

-csc(x)cot(x)

Answer 8

And when you get that, you add the two together.

When you do a derivative of something in the dorm of
\[\Large y=f(x)\]
You actually have \[\Large \frac{ dy }{ dx }= f'(x)\]

This is known as implicit differentiation. You will learn it later on. It is the underlying concept as to what you are doing.

Answer 9

So your final answer is -3sin(x)-csc(x)cot(x)

Answer 10

okay so then its just
-3sin(x)-csc(x)cot(x)

Answer 11

It's actually -3sin(x) + (-csc(x)cot(x)) but a positive plus a minus is a minus

Answer 12

thank you very much !!

Answer 13

Great job! Np