Differentiation

Differentiation from First Principles
Differentiation 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 the rate of change of a more general function, it is necessary to take a limit. This is done explicitly for a simple quadratic function.Length: 30 minutes 
Differentiating Powers of x
Differentiating powers of x. If y=x^n then dy/dx = nx^n1. This result is derived in this video and illustrated with several examples, including cases where n is negative, or is a fraction.Length: 14 minutes 
Differentiating sines and cosines
Differentiating sines and cosines. This video covers the differentiation of sin x and cos x from first principles.Length: 14 minutes 
Differentiating logs and exponents
Differentiating logs and exponentials. This unit gives details of how logarithmic functions (ln x) and exponential functions (e^x) are differentiated.Length: 26 minutes 
Using a Table of Derivatives
Using a table of derivatives. This video looks at 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, are explored. The table is extended using the chain rule for differentiation.Length: 20 minutes 
The Quotient rule
The quotient rule. This is a special rule that may be used to differentiate the quotient of two functions.Length: 16 minutes 
The Product Rule
The product rule. This is a special rule that may be used to differentiate the product of two (or more) functions.Length: 13 minutes 
The Chain Rule
The chain rule. This is a special rule that may be used to differentiate a composite function (that is, a function of another function).Length: 24 minutes 
Parametric Differentiation
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 variable, t say, known as a parameter. Functions defined in this way can be differentiated using a technique called parametric differentiation.Length: 21 minutes 
Differentiation by Taking Logarithms
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.Length: 19 minutes 
Implicit 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 are called implicit functions, and they can be differentiated to give dy/dx.Length: 30 minutes 
Extending the Table of Derivatives
Extending the table of derivatives. In this video the Table of Derivatives continues to be built using rules described in other units.Length: 22 minutes 
Tangents and Normals
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 curve at a given point. The normal is a straight line through the point perpendicular to the tangent.Length: 31 minutes 
Maxima and minima
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 points are often associated with the largest or smallest values of the function, at least in their immediate locality.Length: 38 minutes