Question

find the first derivative y=(csc x + cot)(csc x - cot)

Answer 1

Do you know the product rule?

Answer 2

yeah

Answer 3

Do you know the derivatives of those trig functions? :)

Answer 4

no

Answer 5

The derivative this time is 0

Answer 6

y = (csc x + cot x)(csc x - cot x)
= (csc x)^2 - (cotx)^2
= 1 + (cotx)^2 - (cotx)^2
=1

And the derivative of 1 is 0

Answer 7

Maybe he'd like to know how to do it instead of just being given the answer?

Answer 8

how you get the power to the 2 for csc x and cot x?

Answer 9

By simplifying the expression, multiplying what's inside the parenthesis

Answer 10

so i have to use foil?

Answer 11

Yep, use the foil method

Answer 12

ok. i dont understand the csc and cot like what do they equal to?

Answer 13

What do you mean by that? Do you mean what they equal after you multiply them?

Answer 14

like sin x= cos x and cos x = -sinx or tan x= sin x/cos x

Answer 15

csc x = 1/sin x and tan = 1/tan x

Answer 16

No no no! The derivative of csc x is -cosxcotx and the derivative of tan x is sec^2 x. While yes, you can foil this before you find the derivative, you don't have to.

Answer 17

Oh, I got confused for a second there...oops ^^*

Answer 18

Becki is right, but using foil just simplifies the expression to cut back on confusion

Answer 19

so csc x = -cosx cot x and tan x = sec^2? What about sin and cos?

Answer 20

sin x and cos x you had correct. the deriviatives of each of those is cos x and -sin x respectively.

Answer 21

so they equal to each other?

Answer 22

No. When you differentiate sin x, you get cos x. When you differentiate cos x, you get -sin x.

Answer 23

oooh ok but what about dividing cos x and sin x?

Answer 24

Dividing them by what?

Answer 25

cos x / sin x

Answer 26

That's the definition of cot x.

Answer 27

i though it equal to tan x

Answer 28

Here's what i got for your original question. I went ahead and foiled it since you probably already did that. Then I used the chain rule to differentiate.

Answer 29

how you get (2cot x)? i though the 2 supposed to be on the outside of the parentheses

Answer 30

never mind