Différenciation
Dérivées et techniques de différenciation
Interactive Differentiation Visualization
Welcome to the Differentiation Explorer
This interactive visualization helps you understand differentiation rules and see how derivatives relate to the original function. Explore seven different function types covering all major differentiation rules.
What you can explore:
- Polynomial functions - Learn the Power Rule with f(x) = x³
- Trigonometric functions - See how sin(x) differentiates to cos(x)
- Exponential functions - Discover why e^x is its own derivative
- Logarithmic functions - Understand the derivative of ln(x)
- Product Rule - Explore f(x) = x²·sin(x) and see how products are differentiated
- Quotient Rule - Learn to differentiate f(x) = x²/(x+1)
- Chain Rule - Master composite functions with f(x) = sin(x²)
How to Use This Visualization
Interactive Features:
- • Select Function Type - Choose from 7 different functions to explore various differentiation rules
- • Adjust Point x - Use the slider or click on the graph to set the point where you want to see the derivative
- • Toggle Visualizations - Show/hide the derivative curve, tangent line, and slope triangle
- • View Steps - Enable step-by-step differentiation process to see how each rule is applied
What You'll See:
- • Function Curve (solid, colored) - The original function f(x)
- • Derivative Curve (dashed red) - The derivative f'(x) when enabled
- • Tangent Line (green) - Shows the slope at the selected point
- • Slope Triangle (blue) - Visual representation of rise over run
- • Current Values - Real-time display of x, f(x), f'(x), and slope
- • Differentiation Steps - Step-by-step breakdown of how to differentiate
Power Rule: d/dx(xⁿ) = nxⁿ⁻¹
Click on the graph to set x
Current Values
x: 1.00
f(x): 1.0000
f'(x): 3.0000
Slope: 3.0000
Differentiation Rule
Power Rule: Power Rule: d/dx(xⁿ) = nxⁿ⁻¹
f'(x) = 3x²
Common Differentiation Rules
Power Rule:
d/dx(xⁿ) = nxⁿ⁻¹
Product Rule:
(fg)' = f'g + fg'
Quotient Rule:
(f/g)' = (f'g - fg') / g²
Chain Rule:
d/dx[f(g(x))] = f'(g(x))·g'(x)
Trigonometric:
d/dx(sin x) = cos x
d/dx(cos x) = -sin x
Exponential/Log:
d/dx(e^x) = e^x
d/dx(ln x) = 1/x
Leçons
Unités d'apprentissage individuelles
Leçons à venir