# Slope of the tangent line, Calculus

Find the slope of tangent line to the curve at the point $(1, \pi/2)$

the equation is $$\sin(xy) = x$$

The right answer was = Slope is infinite

My answer was taking the derivative and I end up in this equation

$$(1-y\cos(xy))/ x\cos(xy)$$

I substitute with the points and the calculator showed an error, Does the error means infinite ?

The calculator shows an error, because when you substitute (1,$$\frac{\pi}{2}$$), you're dividing by 0, which isn't allowed.
This means that we have to plot the function in order to see what's going on at the point (1,$$\frac{\pi}{2}$$).
We see that in ($$1,\frac{\pi}{2}$$), the slope is vertical, and that means that the slope is infinite.