Derivatives of Functions in Parametric Forms

The video tutorial explains derivatives of functions in parametric forms, introducing the concept of parametric functions where a third variable, the parameter, is used to express the relationship between two variables. The chain rule is used to find derivatives of these functions. The tutorial includes examples with trigonometric and quadratic functions, demonstrating how to calculate dy/dx by differentiating with respect to the parameter and applying the chain rule.

What is the role of a parameter in parametric functions?

• It is used to express the relationship between two variables.

• It is the integral of the function.

• It is the derivative of the function.

• It acts as a constant in the function.

Which rule is used to find the derivative of parametric functions?

• Power Rule

• Chain Rule

• Quotient Rule

• Product Rule

In the example where x = a sin(θ) and y = a cos(θ), what is the derivative dy/dx?

• tan(θ)

• -cos(θ)

• -tan(θ)

• sin(θ)

For the parametric equations x = kt² and y = 2kt, what is the derivative dy/dx?

• t²

• 1/t

• 2k

• 2t

In the example with x and y in terms of θ, what is the expression for dy/dx?

• sec(θ) + tan(θ)

• tan(θ) - sec(θ)

• sin(θ) - cos(θ)

• cos(θ) + sin(θ)