Differentiation (3)

• July 6th 2008, 07:46 PM
Tangera
Differentiation (3)
Hello!

If sin y = 2 sin x, show that (dy/dx)^2 = 1 + 3 sec^2 y

I tried implicit differentiation and I found dy/dx = 2 cos x / 2 cos y, but I don't know how to continue from there...

Thank you for helping!!
• July 6th 2008, 08:25 PM
kalagota
Quote:

Originally Posted by Tangera
Hello!

If sin y = 2 sin x, show that (dy/dx)^2 = 1 + 3 sec^2 y

I tried implicit differentiation and I found dy/dx = 2 cos x / 2 cos y, but I don't know how to continue from there...

Thank you for helping!!

$
\frac{dy}{dx} = \frac{2\cos x}{\cos y}$

$
\left(\frac{dy}{dx}\right)^2 = \frac{4\cos^2 x}{\cos^2 y}$

what is $\cos^2 x =?$