Control-drag the equation of the circle.

Context Panel: Differentiate≻Implicitly
(See explanation in next cell, below.)

After selecting "Implicitly" in the Context Panel, the dialog box shown in Figure 2.5.2(a) opens. Select $y$ as the dependent variable. "Differentiate with respect to" x.

The result of the calculation matches the outcome found in Example 2.5.1, provided the letter $y$ in the implicit derivative is replaced by $\sqrt{9-x^2}$, the explicit expression for $y_{\+}\left(x\right)$.

Note that $-x\/y$ represents the derivative $y_{\+}$ and $y_{-}$; simply replace $y$ with $y_{\pm }\left(x\right)$, as appropriate.

After entering the problem details, the Execute button returns the same derivative as the Context Panel.

The Stepwise Calculation illustrates the four basic steps of implicit differentiation. First, each letter $y$ is replaced by $y\left(x\right)$; then, the expression is differentiated with respect to $x$. The term $y{\left(x\right)}^2$ is differentiated with the Chain rule.

Clicking the Stepwise button launches the  tutor with the differentiation problem

In the third step, the derivative $y\prime \left(x\right)$ is isolated.

In the final step, $y\left(x\right)$ is restored to the letter $y$.

Control-drag (or type) the equation of the circle.

Context Panel: Evaluate at a Point≻$y\=y\left(x\right)$

Context Panel: Differentiate≻With Respect To≻$x$

Context Panel:
Solve≻Isolate Expression for≻$\mathrm{diff}\left(y\left(x\right)\,x\right)$