#### CHECK OUT SHMOOP'S FREE STUDY TOOLS: Essay Lab | Math Shack | Videos

# Computing Derivatives

# Computing Derivatives Topics

## Computing Derivatives explanations, examples, practice problems. Ready? Let’s do this.

#### Derivatives of Basic Functions

In this section we'll find derivatives of functions that a pop up all the time. Unlike pop-up ads, they won't be blocked. Almost all derivative problems will use one of these functions. We'll look...

#### Derivatives of More Complicated Functions

Since most functions are complicated, we need some more rules. Next: how to find derivatives of functions that were built by taking sums, products, and quotients of simpler functions. The "prime" n...

#### Derivative of a Sum (or Difference) of Functions

The derivative of a sum is the sum of the derivatives:
(f + g)' = f' + g'.
When the function has more than two terms, and some weird combination of addition and subtraction, the process is similar....

#### Derivative of a Product of Functions

Use the product rule whenever there is a function that's a product of two other functions of x. Iff(x) = ({something with an x}) × ({something else with an x}),then use the product rule to find f'...

#### Derivative of a Quotient of Functions

Division within derivatives is more complicated that the other rules we've seen so far. Make some space in the ol' memory bank for the Quotient Rule. The Quotient Rule states that the derivati...

#### Solving Derivatives

There are a lot of rules floating about now. Besides knowing how to take the derivatives of less complicated functions, we have all these rules for taking the derivatives of more complicated functi...

#### Derivatives of Even More Complicated Functions

How do we find the derivative of a function that's made of one function nested inside another, likeesin xor(ln x)42The tool we need is called the Chain Rule. While the chain rule isn't always likea...

#### Patterns

Combining the derivatives of basic functions with the chain rule gives us a lot of patterns that let us take derivatives of functions that seem complicated. Sample Problem Let h(x) = e{cos x}. If w...

#### Implicit Differentiation

Now it's time to throw a monkey wrench into the works, curve ball style. What happens when we mix two variables together, on both sides of the equation? Why calculus? Why?! We're entering the Twili...

#### In the Real World

In computer programming there's an idea called "top-down design" or "stepwise refinement." This is essentially the art of breaking a big problem down into little problems, then breaking the little...