Parametric & Implicit Differentiation

Some curves are not written directly as y in terms of x.

Parametric and implicit differentiation help find $\frac{dy}{dx}$ for those curves.

These methods are used in calculus, physics, motion, geometry, and curve analysis.

Parametric equations express x and y using a third variable, often t.

For parametric curves, $\frac{dy}{dx}$ = ($\frac{dy}{dt}$)/($\frac{dx}{dt}$), when $\frac{dx}{dt}$ is not zero.

Implicit equations mix x and y in one equation, such as $x^{2} + y^{2} = 25$.

In implicit differentiation, y is treated as a function of x.

Whenever y is differentiated, include $\frac{dy}{dx}$.

You will learn

• Understand parametric equations.
• Find $\frac{dy}{dx}$ from $\frac{dx}{dt}$ and $\frac{dy}{dt}$.
• Differentiate implicit equations.
• Use chain rule with y as a function of x.
• Avoid treating y as a constant.