Question

y = (sec x + tan x)(sec x - tan x)

y' = ?

Answer 1

Bovice, would you agree that the first step is to multiply it out?

Answer 2

And also, are you telling me your teacher never showed you how to take the derivative of (sec x)^2 ?

Answer 3

Go ahead Ishaan. Clearly he doesn't want my help anymore.

Answer 4

\[y =sec^2x - tan^2x \]
\[\frac{dy}{dx} = 2*secx^{2 -1}*(secx*tanx) -2*tanx^{2-1}*(sec^2x)\]
\[y' = 2sec^2x*tanx - 2sec^2x*tanx = 0 \]
Hero's method...

Answer 5

we are not using that method
that method has NOT been taught yet

Answer 6

this problem can be solved WITHOUT using the chain rule

Answer 7

Bovice, please just answer my question. Did your teacher show you how to take the derivative of (sec x)^2

Answer 8

(sec x + tan x)(sec x - tan x) = (1 - sin²x)/cos²x

Answer 9

now solve it....

Answer 10

yes it is

Answer 11

I mean It's the same

Answer 12

in both cases the answer is 1

Answer 13

so the derivative of 1 = 0

Answer 14

Well, at least you were able to solve it

Answer 15

of course, you could have substituted the top

1-sin^2x = cos^2 x


cos^2x/cos^2x = 1

Answer 16

Good job bovice.

Answer 17

i've seen that rule before....

cos²x = 1 - sin² x ?

right?

Answer 18

Yes

Answer 19

\[sec^2x = 1 + tan^2x \]

\[sec^2x - tan^2x =1 \]

Answer 20

now i understand the problem....

you have y = cos²x / cos²x

y = 1

y' = 0

Answer 21

Sorry, I don't have all the identities memorized Ishaan

Answer 22

ishann's identities dont help but they can be rearranged...

Answer 23

I must admit, that's a terrible admission

Answer 24

Well had I known that, we would have arrived at the same conclusion without chain rule

Answer 25

It helps. You should add that identity to your memory bank

Answer 26

Use of Identities definitely helps

Answer 27

again, this answer didnt need the chain rule, nor was it helpful to introduce the chain rule....this question was all about rearranging the original equation before differentiating....thank you and good night lol

Answer 28

I apologize for making you angry. It wasn't my intention. I only used chain rule because I couldn't remember the identity. Sorry bro. I think you got plenty of help here though. Feel free to come here anytime you need help

Answer 29

not angry....frustrated

Answer 30

Oh. Well, we got it and you did a good job getting there. For some reason you came here even though you managed to actually get the solution on your own. We need more students here like you who actually try to think for themselves. Maybe you figuring it out on your own was meant to be.