See calculus concepts come to life with interactive graphs, animations, and 3D visualizations
The derivative at a point is the slope of the tangent line to the curve at that point. As the secant line approaches the tangent line, the slope approaches the derivative.
The chain rule is easier to understand visually. When you have f(g(x)), you're applying one function to the result of another.
Chain Rule: f'(x) = f'(g(x)) · g'(x)
For sin(x²): cos(x²) · 2x
Think of u(x) and v(x) as sides of a rectangle. The product u·v is the area. When both sides change, the change in area has two parts.
The quotient rule shows how the ratio u/v changes when both numerator and denominator change.
For functions of two variables, partial derivatives show how the function changes when you move in just the x-direction or y-direction.
The gradient ∇f points in the direction of steepest ascent. The length shows how steep the slope is.
Watch secant lines become tangent lines
Visualize derivatives as changing slopes
See function composition visually
Area interpretation of product rule
Interactive tool to visualize tangent lines on any function.
Visual diagnostics for common derivative errors.
Step-by-step visual solutions to complex problems.
Terms explained with diagrams and animations.
Use our graphing calculator with visual outputs.
Complete visual learning resources for calculus.