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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 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"...

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 know the derivative of each function.The derivative of a sum is just the sum of the derivatives: (...

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 x2ex.For the first expression, we know how to find the derivatives of 3x and sin x, but we don't yet...

Derivative of a Quotient of Functions

Division within derivatives is more complicated than 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 deriva...

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 func...

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)42?The tool we need is called the Chain Rule. While the chain rule isn't always li...

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) = ecos 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 Twi...

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 littl...
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