Movies

Derivatives

The definition of a derivative can be explained though geometry within just a few minutes. Take a look and judge for yourself.

Addition

Derivatives of two added functions are the basic building block upon which the rest of the calculus concepts are founded. It is often explained in a belabored and confusing manner but you should be able to get the gist of it by simply watching a few minutes of this video.

Multiplication

When we were first told about multiplication images of rectangles and squares were drawn as geometric representations of multiplications. This video uses this geometric analogy to quickly explain a derivative of a multiplication function.

Division

Division was often represented as a rate or a ratio when we were first introduced to a concept. This short video uses the sides of two similar triangles to easily explain how the derivative of a division changes as each side of the triangle changes.

Trigonometry ( Sin, Cos, Tan )

The derivatives of trigonometric functions (Sin, Cos, Tan) are some of the most mysterious and least understood by most calculus students. This is an especially unfortunate situation since the derivatives of these functions are some of the easiest to understand through geometry. Hopefully you will enjoy discovering the real meaning behind trigonometric derivatives while watching this video.

Inverse Functions

The derivatives of inverse functions should be related to the derivatives of the original functions. The relationship between the two isn’t necessarily obvious at first but it becomes clear once we analyze it geometrically.

Functions Within Functions

If there is a function within another function then the derivative of the final function should have something to do with the derivatives of the original functions. Knowing the exact way in which the original derivatives are related to the final derivative would help us understand the derivatives of very complicated functions. Luckily for us a geometric analysis helps us better understand these relationships.

Exponents Part One

The study of derivatives of Exponential functions is a bit more involved topic then all of the previous ones that we covered. Instead of presenting the general case that covers the derivatives of all exponential functions, in this part we will only cover the derivatives of exponents that are whole numbers (1, 2, 3, 4,… )

Exponents Part Two

The study of derivatives of Exponential functions is a bit more involved topic then all of the previous ones that we covered. Instead of presenting the general case that covers the derivatives of all exponential functions, in this part we will take an in depth look and present an alternative combinatorial explanation for the derivatives of exponents that are whole numbers (1, 2, 3, 4,… )

Exponents Part Three

The study of derivatives of Exponential functions is a bit more involved topic then all of the previous ones that we covered. Instead of presenting the general case that covers the derivatives of all exponential functions, in this part we will take an in depth look at only the negative and fractional exponents. Our previous geometric proofs are used to show that the same derivative rule applies to exponents that are whole numbers as well as negative and fractional numbers.

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