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How to find $\frac{dy}{dx}$ using implicit differentiation?

Differentiate both sides with respect to $x$ . 2. Apply chain rule to y terms. 3. Isolate $\frac{dy}{dx}$ .

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How to find $\frac{dy}{dx}$ using implicit differentiation?

Differentiate both sides with respect to $x$ . 2. Apply chain rule to y terms. 3. Isolate $\frac{dy}{dx}$ .

How to find the tangent line equation at a point?

Find $\frac{dy}{dx}$ at the point. 2. Use point-slope form: $y - y_1 = m(x - x_1)$ .

What does $\frac{dy}{dx} = 0$ indicate on a graph?

A horizontal tangent line, indicating a local maximum or minimum (or saddle point).

What does the sign of $\frac{dy}{dx}$ tell you?

Positive: the function is increasing. Negative: the function is decreasing.

What is implicit differentiation?

A method to find derivatives when $y$ is not explicitly defined in terms of $x$ .

What is $\frac{dy}{dx}$ in implicit differentiation?

Represents the derivative of $y$ with respect to $x$ , found when $y$ is not explicitly defined.