implicit differentiation, tangent line help

Sep 2008
631
2
Find the equation to the tangent and the normal to the curve \(\displaystyle sinx siny = \frac{\sqrt{3}}{4} \)

at the point ( \(\displaystyle \frac{\pi}{3} , \frac{\pi}{6} \) )

I keep getting this question wrong, here's my working;

using the product rule on sinxsiny
\(\displaystyle sinx cosy \frac{dy}{dx} + siny cosx = 0 \)

\(\displaystyle \frac{dy}{dx} = -\frac{ siny cosx}{sinx cosy} \)

Is this part correct?
 
Oct 2009
4,261
1,836
Find the equation to the tangent and the normal to the curve \(\displaystyle sinx siny = \frac{\sqrt{3}}{4} \)

at the point ( \(\displaystyle \frac{\pi}{3} , \frac{\pi}{6} \) )

I keep getting this question wrong, here's my working;

using the product rule on sinxsiny
\(\displaystyle sinx cosy \frac{dy}{dx} + siny cosx = 0 \)

\(\displaystyle \frac{dy}{dx} = -\frac{ siny cosx}{sinx cosy} \)

Is this part correct?

Yes, it is. Now just note that \(\displaystyle \frac{\cos x\sin y}{\sin x\cos y}=-\frac{\tan y}{\tan x}\) ...

Tonio
 
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