MHB What is the equation of the tangent line at (π/2,1) for sin(xy)=y?

[karush]

Find the equation of the line tangent to
$$\sin\left({xy}\right)=y$$
At point
$$\left(\frac{\pi}{2 },1\right)$$
Answer $y=1$

I didn't know how to deal with xy.
No example given

 

[Ackbach]

You need to differentiate implicitly, treating $y$ as $y(x)$. So, you'd start out with:
$$\d{}{x}\left[ \sin\left({xy}\right)=y \right] \qquad \implies \qquad \cos(xy) \cdot \left(y+xy'\right)=y'.$$
Can you continue from here?

 

[karush]

Isolating $y'$ I got $$y '=\frac{-\cos\left({xy}\right)y}{x\cos\left({xy}\right)-1}$$
Plug in $$\left(\frac{\pi}{2 }, 1\right)\ \ y' =0$$
So $y=1$ is the equation