Differentiation

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14 videos in this playlist

Differentiation From First Principles
What is differentiation? It is about rates of change -- for example, the slope of a line is the rate of change of y with respect to x. To find…
Differentiating Powers of x
If y=x^n then dy/dx = nx^n-1. This result is derived in this unit and illustrated with several examples, including cases where n is negative, or is a fraction.
Differentiating Sines and Cosines
This unit covers the differentiation of sin x and cos x from first principles.
Differentiating Logs and Exponentials
This unit gives details of how logarithmic functions (ln x) and exponential functions (e^x) are differentiated.
Using a Table of Derivatives
The construction of a Table of Derivatives of common functions using differentiation from first principles. Linearity rules for constant multiples of functions and for sum/difference of two functions, with examples,…
The Quotient Rule
A special rule, the quotient rule, may be used to differentiate the quotient of two functions.
The Product Rule
A special rule, the product rule, may be used to differentiate the product of two (or more) functions.
The Chain Rule
A special rule, the chain rule, may be used to differentiate a composite function (that is, a function of another function).
Parametric Differentiation
Instead of a function y(x) being defined explicitly in terms of the independent variable x, it is sometimes useful to define both x and y in terms of a third…
Differentiation by Taking Logarithms
The logarithm of a product is a sum, and so logarithms can be used to simplify certain functions for the purpose of differentiation.
Implicit Differentiation
Sometimes functions are not given in the form y = f(x) but in a more complicated form where it is difficult to express y explicitly in terms of x. These…
Extending the Table of Derivatives
In this unit the Table of Derivatives continues to be built using rules described in other units.
Tangents and Normals
This unit explains how differentiation can be used to calculate the equations of the tangent and normal to a curve. The tangent is a straight line which just touches the…
Maxima and Minima
Because the derivative provides information about the gradient of a graph of a function, we can use it to locate points on a graph where the gradient is zero. Such…

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