Study Guide

Computing Derivatives Topics

Derivatives of Basic Functions

The first kind of function is a constant function.If f(x) = C for some constant C, then f ' (x) =...

Derivatives of More Complicated Functions

Since most functions are complicated, we need some more rules. Next: how to find derivatives of...

Derivative of a Sum (or Difference) of Functions

Anytime we add two functions, we can find the derivative of the sum pretty easily, so long as we...

Derivative of a Product of Functions

There's a convenient rule we can use to find the derivative of expressions like (3x)(sin x) or...

Derivative of a Quotient of Functions

Division within derivatives is more complicated than the other rules we've seen so far. Make some...

Solving Derivatives

There are a lot of rules floating about now. Besides knowing how to take the derivatives of less...

Derivatives of Even More Complicated Functions

How do we find the derivative of a function that's made of one function nested inside another,...

Patterns

Combining the derivatives of basic functions with the chain rule gives us a lot of patterns that...

Implicit Differentiation

Now it's time to throw a monkey wrench into the works, curve ball style. What happens when we mix...

In the Real World

In computer programming there's an idea called "top-down design" or "stepwise refinement." This...

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