6. Topic 6(COLON) Advanced Calculus

Lesson 6.3: Implicit And Parametric Differentiation — Quiz

Test your understanding of lesson 6.3: implicit and parametric differentiation with 5 practice questions.

Practice Questions

Question 1

What is the derivative of the implicit relation $x^2 + y^2 = 25$ with respect to $x$?

Question 2

If the curve is defined parametrically by $x = t^2$ and $y = t^3$, what is $\frac{dy}{dx}$ in terms of $t$?

Question 3

For the parametric equations $x = t^2 + 1$ and $y = t^2 - 3t$, what is the second derivative $\frac{d^2y}{dx^2}$ evaluated at $t = 2$?

Question 4

Given the implicit relation $xy + 4 = 0$, what is $\frac{dy}{dx}$?

Question 5

If $y = 2\sin(t)$ and $x = 3\cos(t)$, what is $\frac{dy}{dx}$?