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Thread: implicit differentiation, tangent line help

  1. #1
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    implicit differentiation, tangent line help

    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?
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  2. #2
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    Quote Originally Posted by Tweety View Post
    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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