Simple Derivative Calculator
Advanced Derivative Calculator with Graph
Online Derivative Calculator – Instant Differentiation with Graph
Welcome to the free online Derivative Calculator – a powerful and easy-to-use tool that helps you compute the derivative of any mathematical function in seconds.
- Differentiate functions with respect to any variable (x, y, t, etc.)
- Get simplified output instantly
- Visualize original and derivative graphs (advanced)
- Use trigonometric, exponential, logarithmic, rational, and polynomial expressions
What is a Derivative?
A derivative represents the rate of change or slope of a function. In simple terms, it tells you how fast something is changing at any point.
Derivative Formula
If \( f(x) \) is a function, then the derivative of \( f \) with respect to \( x \) is:
\( f'(x) = \frac{d}{dx}f(x) \)
Common Derivative Rules
Rule | Formula |
---|---|
Power Rule | \( \frac{d}{dx}x^n = nx^{n-1} \) |
Constant Rule | \( \frac{d}{dx}c = 0 \) |
Sum Rule | \( \frac{d}{dx}(f + g) = f’ + g’ \) |
Product Rule | \( \frac{d}{dx}(fg) = f’g + fg’ \) |
Quotient Rule | \( \frac{d}{dx}\left(\frac{f}{g}\right) = \frac{f’g – fg’}{g^2} \) |
Chain Rule | \( \frac{d}{dx}f(g(x)) = f'(g(x)) \cdot g'(x) \) |
Trigonometric | \( \frac{d}{dx}\sin(x) = \cos(x), \quad \frac{d}{dx}\tan(x) = \sec^2(x) \) |
Examples
- \( \frac{d}{dx}(x^2 + 3x) = 2x + 3 \)
- \( \frac{d}{dx}(\sin(x)) = \cos(x) \)
- \( \frac{d}{dx}(e^x) = e^x \)
- \( \frac{d}{dx}(\ln(x)) = \frac{1}{x} \)
Features of This Calculator
Feature | Simple Version | Advanced Version |
---|---|---|
Supports polynomials, sin, cos, log, exp | ✔️ | ✔️ |
Custom variable (x, y, t…) | ✔️ | ✔️ |
Step-by-step output | ✔️ | ✔️ |
Graph plotting | ❌ | ✔️ |
LaTeX Math Output | ❌ | ✔️ |
Mobile friendly | ✔️ | ✔️ |
Use Cases
- ✅ For class 11/12 students studying calculus
- ✅ For engineering and science students
- ✅ For quick homework checks
- ✅ For plotting and visualizing changes
How It Works
- Enter the function like
x^3 + 2x
- Specify the variable (default is
x
) - Hit “Calculate”
- View the simplified derivative
- (Advanced only) View the graph of
f(x)
andf'(x)
Supported Functions
- Algebra:
x^2
,3*x + 2
,(x + 1)^3
- Trigonometry:
sin(x)
,cos(x)
,tan(x)
- Exponential:
e^x
,2^x
- Logarithms:
ln(x)
,log10(x)
- Combinations:
x^2 * sin(x)
,ln(x^2 + 1)