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implicit differentiation

smooo

does x = sec 2 y differentiate to 2 dy/dx sec y tan y ?

Reply 1

Zacken

Original post by smooo

does x = sec 2 y differentiate to 2 dy/dx sec y tan y ?

If you differentiate it with respect to x, sure.

Reply 2

smooo

Original post by Zacken

If you differentiate it with respect to x, sure.

thank you

Reply 3

Zacken

Original post by smooo

thank you

Reply 4

Zacken

Original post by smooo

thank you

Please ignore my previous post, I was busy and missed something. The correct expression (if differentiating w.r.t x) should be

2 \frac{dy}{dx} \sec 2y \tan 2y

.

I'm incredibly sorry.

Reply 5

smooo

Original post by Zacken

Please ignore my previous post, I was busy and missed something. The correct expression (if differentiating w.r.t x) should be

2 \frac{dy}{dx} \sec 2y \tan 2y

.

I'm incredibly sorry.

Don't worry about it

Reply 6

Zacken

Original post by smooo

Don't worry about it

Thanks, so you can see that you get

\dfrac{dy}{dx} = \frac{1}{2\sec 2y \tan 2y}

yeah?

But you know that

\sec 2y = x

and you know that

1 + \tan^2 2y = \sec^2 2y = x^2 \Rightarrow \tan 2y = \sqrt{x^2 - 1}

.

So

\frac{dy}{dx}

can be found as a function of

x

Reply 7

smooo

Original post by Zacken

Thanks, so you can see that you get

\dfrac{dy}{dx} = \frac{1}{2\sec 2y \tan 2y}

yeah?

But you know that

\sec 2y = x

and you know that

1 + \tan^2 2y = \sec^2 2y = x^2 \Rightarrow \tan 2y = \sqrt{x^2 - 1}

.

So

\frac{dy}{dx}

can be found as a function of

x

thanks a lot, sorry for putting you through so much trouble.

Reply 8

Zacken

Original post by smooo

thanks a lot, sorry for putting you through so much trouble.

no no it's my fault for not checking more carefully :tongue:

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