Enter your parametric expressions below:

Use the buttons below to enter your expression:

CLR

−

√

f(x)

(

)

Set your Configurations:

Derivative variable

Order of the derivative

1 (first)

Derivative at Point

Your input will be Calculated as:

Click an Example button to insert parametric equations into both X(t) and Y(t) input boxes.

Parametric Function Derivative Calculator

Find Derivatives of Parametric Equations with Steps & Graphs!

Use our parametric derivative calculator to compute derivatives of parametric functions like (x(t), y(t)) step-by-step. It applies the rule below and displays each step of the process with explanation and graphs.

Why Use a Parametric Derivative Calculator?

Step-by-step derivative calculations from parametric equations.
Automatically applies the chain rule for parametric forms.
Interactive graph of parametric curves with tangent line.
Useful for physics, engineering, and calculus problems.
Supports trigonometric, exponential, and logarithmic parameterizations.

How to Use the Parametric Derivative Calculator?

Enter the parametric functions x(t) and y(t) .
Select the parameter variable (usually t).
Optionally input a point to evaluate the derivative at a specific value of t .
Click the Go! button.
Review step-by-step results and the plotted curve.

What Is a Parametric Derivative?

A parametric derivative expresses the slope (dy/dx) in terms of a third variable, (usually time t), by computing (dy/dt)/(dx/dt) This approach is essential when functions are given in parametric form. Learn more on our.Parametric Functions notes page.

Common Use Cases of Parametric Derivatives

Analyzing particle motion in physics and kinematics.
Graphing curves that loop or intersect themselves.
Calculating slopes on implicit curves via parametric representation.
Modeling real-world paths and trajectories.

Features of Our Calculator

Fast & accurate parametric differentiation
Clear step-by-step breakdown of each derivative
Dynamic plotting of (x(t), y(t)) with tangent lines
Free to use and accessible on all devices
Integrated with our advanced math tools for further exploration

Dive deeper with our full derivative notes and visit our help section or FAQs if you have any questions.