Working left to right, we have:

Derivative of `2y`:


Derivative of `5` is `0`.

Derivative of x2 is `2x`.

Derivative of y3:


Putting it together, implicit differentiation gives us:


Collecting like terms gives:




Now, when `x = 2` and `y = -1`,




So the slope of the tangent at `(2,-1)` is `-4`.

Let's see what we have done. We graph the curve


and graph the tangent to the curve at `(2, -1)`. We see that indeed the slope is `-4`.

It works!

implicit graph