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Find the tangent plane to $z=x\sin(y/x)$ in $(a,b,a \sin(b/a))$

I got: $\pi) x[\sin(b/a)-\frac{b\cos(b/a)}{a}]+y \cos(b/a)-z=0$

Can somebody check the answer?

amWhy
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Damian Ariel
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  • This site can be useful for checking answers: www.wolframalpha.com/examples/TangentsNormals.html – Dave Nov 09 '16 at 23:29
  • This doesn't look right (it's unlikely that all the constants cancelled). See the formula in the answer below. – Michael Burr Nov 09 '16 at 23:34

1 Answers1

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The tangent (affine) plane to $z=F(x,y)$ at $(a,b,F(a,b))$ is given by

$$F(a,b)+\frac{\partial F}{\partial x}(a,b)(x-a)+\frac{\partial F}{\partial y}(a,b)(y-b)=z$$

I don't understand what you wrote, but as long you know the basic rules of derivatives you should be fine!

Sonner
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