DERIVATIVES
Limits taught us how to zoom in infinitely close. Now, we use that power to measure Instantaneous Change.
Every point on a curve has a secret direction. The Derivative reveals it.
Don't Memorize. Visualize.
The red line is the Tangent Line. Its slope tells you exactly how fast the function is growing or shrinking at that specific moment.
Notice how the slope is 0 at the peaks and valleys? That's not a coincidence. That's optimization.
Curriculum
5 ModulesThe Tangent Problem
Constructing the derivative from the secant line limits.
Power & Sum Rules
Learn the patterns that let you differentiate polynomials in seconds.
Product & Quotient Rules
Handling functions that are multiplied or divided.
The Chain Rule
The most important rule in Calculus. Peeling the onion of composite functions.
Implicit Differentiation
Finding slopes of weird shapes (circles, ellipses) where y cannot be isolated.
Notation Decoder
f'(x)"F prime of x". Best for general functions. Shows that the derivative is itself a function.
dy/dx"The change in y divided by the change in x". Best for remembering that slope is a ratio.
Dx[y]"The derivative operator". Best for thinking of differentiation as an action you perform.