What is a Derivative?
Learn how things change in a split second! It's like seeing how fast a superhero accelerates in a movie.
The Power Rule
This is a math superpower! It’s the fastest way to solve calculus puzzles and save the day without breaking a sweat.
The Quotient Rule
Fractions are tricky, but the Quotient Rule makes dividing functions a piece of cake instead of a headache.
Zooming Deeper: Double Derivatives
Go even deeper! Acceleration is just the derivative of speed. It's like seeing how fast the 'fast' is changing!
The Speed Trap: Mean Value Theorem
This theorem promises that at some point, you must have hit your exact average speed! No escaping the truth.
Newton's Method
Newton’s Method is like using smart guessing to find where a graph crosses the x-axis. Starting from a rough guess, watch how calculus turns a bad estimate into a really accurate solution.
The Mechanics of Differentiation Topic Library
The Rollercoaster Curve: Moving with Graphs
Discover the slope of a curve. We'll show you how to find out if a hill is getting steeper or flatter as you zoom along!
The Sum Team: Plus and Minus
Finding derivatives for added or subtracted parts is as simple as doing them one by one like a relay team.
The Chain Rule
Like a set of nesting dolls, the Chain Rule helps us find derivatives of functions hidden inside other functions.
The Knot Untangler: Implicit Differentiation
Sometimes variables are messy knots. This special rule helps us untangle them and find the speed of change.
First Derivative Test
Calculus helps you find the highest peak or lowest valley in a race. Perfect for choosing the best way to win!
Instant Speed
Forget averages! This is about how fast something is moving at this exact tiny moment in time, just like a radar gun trap.
The Math Mashup: The Product Rule
When two functions have a math baby, we use this special mashup rule to figure out how it changes as a whole.
Trig Curves and Derivatives
Sine and Cosine make beautiful waves! We’ll find the secret speed of their high peaks and low valleys.
Balloon Math: Related Rates
If you blow up a balloon, its size and air volume change together. Track how they're related using cool math.
Second Derivative Test
Learn how the Second Derivative Test acts like a curve detective. You’ll use the second derivative to tell if a critical point is a peak, a valley, or a flat spot, and see how concavity helps you understand the shape and behavior of a function.