Example: Graph the Derivative of x^2
For x^2, the grapher plots f(x)=x^2 and f'(x)=2x together. The parabola changes from decreasing to increasing exactly where the derivative crosses zero.
Derivative Grapher
Plot a function, graph its derivative, and compare how f(x) and f'(x) behave on the same coordinate plane.
Interactive Derivative Grapher
Quick examples
Turn on the tangent line to inspect slope at a specific x-value.
f(x)
x^2
f'(x)
Waiting for a valid derivative...
Function and Derivative Graph
Show original function f(x)Show derivative f'(x)Show tangent line
Need the exact derivative formula first? Use our Derivative Calculator to calculate derivatives step by step.
What Is a Derivative Grapher?
A derivative grapher is a visual derivative graph calculator that plots both a function and its derivative. Instead of only returning a symbolic formula, it helps you graph f and f prime together so you can see how slope changes across the curve.
When you graph derivative behavior, positive derivative values show where the original function increases, negative values show where it decreases, and zeros often line up with turning points. That makes a derivative grapher useful for students, teachers, and anyone learning how to plot derivative relationships.
How to Use the Derivative Grapher
- Enter a supported function such as x^2, x^3, sin(x), cos(x), tan(x), e^x, ln(x), or sqrt(x).
- The tool automatically computes the derivative with the existing symbolic engine and prepares both expressions for graphing.
- Compare the original function and derivative curve on the same graph to understand slope, turning points, and overall derivative behavior.
- Optionally enable the tangent line to inspect how the derivative controls the local slope at a chosen x-value.
Derivative Graph Examples
Example: Graph the Derivative of sin(x)
For sin(x), the derivative grapher shows cos(x) as the derivative curve. This lets you see why the slope of sin(x) is highest near x=0 and zero at its peaks and troughs.
Example: Graph the Derivative of e^x
For e^x, both the function and its derivative stay positive and keep increasing. This is a clear example of a function whose derivative graph has the same overall shape as the original.
Why Graph Derivatives?
When you plot derivative information instead of only reading formulas, you can instantly connect algebra to geometry. A derivative graph shows where a function rises, falls, flattens out, or changes concavity.
That visual feedback makes it easier to understand turning points, tangent lines, and how local slope changes over time. It also helps you verify whether a symbolic answer makes sense before moving on to the next calculus step.
Derivative Grapher vs Derivative Calculator
A derivative grapher focuses on visualization. It helps you graph derivative curves, compare the original function with f'(x), and understand slope behavior on the same chart.
A derivative calculator focuses on the exact formula and often provides symbolic output or step-by-step reasoning. If you want to plot derivative behavior, use the grapher. If you need the precise derivative expression first, use the calculator.