Tangent plane to $z=x sin(y/x)$ in $(a,b,a sin(b/a))$

Question

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?

Answer 1

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!