Loading module…
What you will learn in Differential Calculus
1. Average and Instantaneous Rate of Change
A rate over an interval is a division. A rate at an instant is not, and the difference is where calculus starts.
2. The Derivative as a Limit
The difference quotient, simplified until h has something to cancel with — and then, and only then, sent to zero.
3. The Derivative as a Slope
The secant becoming the tangent, and the third reading of one object.
4. Power, Sum and Constant-Multiple Rules
Three rules, each one a shortcut for work you have already done from the definition.
5. Product and Quotient Rules
Why the obvious guess fails, shown against a numerical derivative rather than asserted.
6. The Chain Rule
Rates multiplying along a pipeline — module 07's composition, differentiated.
7. Derivatives of Trigonometric Functions
sin′ = cos as a consequence of two limits, and what breaks in degrees.
8. Derivatives of Exponential and Logarithmic Functions
Hunting for the base whose exponential is its own derivative, and finding e.
9. Implicit Differentiation
Curves that are not functions, differentiated without being solved first.
10. Parametric Differentiation
A point moving along a curve, with three rates and a velocity vector.
11. Higher-Order Derivatives
The rate of a rate, and why it decides whether a car ride is comfortable.
12. Logarithmic Differentiation
Taking logs first, for the products and powers that no rule handles directly.
13. Rolle's Theorem and the Mean Value Theorem
One theorem with two hypotheses, and what it is holding up in the next module.