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`.