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,$\frac{\pi}{2}$).

Here is a plot: plot

We see that in ($1,\frac{\pi}{2}$), the slope is vertical, and that means that the slope is infinite.

  • $\begingroup$ LOL!! I forgot to post the equation -.-, its edited now. $\endgroup$ – user157908 Jun 23 '14 at 12:36

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