Calculus - Differentiation

Differentiation is the calculus technique for finding the gradient function of an equation.

From this page, you link to all the resources for differentiation of usual functions of x.

References to differentiation of special functions are found elsewhere through:

Resources for integration are accessed from the main menu above or from this hyperlink (because I make it easy for you).

Differentiation resources accessed from this page are:

1. Differentiation by First Principles.

2. Basic techniques of differentiation.

3. The Chain Rule.

4. The Product Rule.

5. The Quotient Rule.

6. Applications of Calculus
(Gradients, tangents and concavity).

7. Implicit Differentiation.

8. Graphing derivative functions.

Learning area.	Resource
1. Differentiation by First Principles.
	First Principles - Test Yourself 1.
	First Principles - Solutions for Test Yourself 1.
2. Basic techniques of differentiation.
	Basic techniques - Test Yourself 1.
	Basic techniques - Test Yourself 1- Solutions.
	Basic techniques - Test Yourself 2.

3. The Chain Rule. The Chain Rule is the first of the three principal techniques used to differentiate a function - after straightforward techniques. The structure of a function to which we apply the Chain Rule comprises: a single bracketed term with an independent variable inside the brackets; the bracket is raised to a power - positive, negative or fractional. The power rarely has a value of 2.
	Chain Rule - Test Yourself 1.
	Chain Rule - Test Yourself 1 - Solutions.
	Chain Rule - Test Yourself 2.
	Chain Rule - Test Yourself 2 - Solutions.

4. The Product Rule. The Product Rule is the second of the three principal techniques used to differentiate a function - after the straightforward techniques. We recognise the structure of a function to which we would apply the Product Rule as comprising: two terms with an independent variable and at least one of the terms inside brackets; the bracket (or brackets) is raised to a power - positive or fractional. The power rarely has a value of 2. Negative indices could be used but normally that case is addressed by our third technique - that of the Quotient Rule. the two terms are multiplied together.
	Product Rule - Test Yourself 1.
	Product Rule - Solutions for Test Yourself 1.
	Product Rule - Test Yourself 2.

5. The Quotient Rule.
	Quotient Rule - Test Yourself 1.
	Quotient Rule - Solutions for Test Yourself 2.
	Quotient Rule - Test Yourself 2.

6. Applications of Differentiation.
First derivative.	Gradients, tangents and normals - Test Yourself 1.
	Gradients, tangents and normals - Test Yourself 1 - solutions.
	Gradients, tangents and normals - Test Yourself 2.
	Gradients, tangents and normals - Test Yourself 2 - solutions.
Second derivative.	Concavity - a note on concept and use.
	Concavity - Test Yourself 1.
	Concavity - Test Yourself 1 - Solutions.
Major maximum and minimum questions.	Link to this page to reference various types of maximum/minimum questions including: application to basic functions to find stationary points, concavity, etc. application of differentiation to practical situations (6 contexts).
7. Implicit Differentiation.
	Implicit Differentiation - Test Yourself 1.
	Implicit Differentiation - Test Yourself 1 - Solutions.

8. Graphing derivative functions.
	Drawing derivative curves from equations and graphs - Test Yourself 1.
	Drawing derivative curves from equations and graphs - Test Yourself 1 - Solutions.
	Derivative curves - interpreting diagrams and statements - Test Yourself 1.
	Derivative curves - interpreting diagrams and statements - Test Yourself 1 - Solutions.
	Drawing primitives from derivative curves - Test Yourself 1.
	Drawing primitives from derivative curves - Test Yourself 1 - Solutions.

9. Differential equations.
	Differential equations - Test Yourself 1.
	Differential equations - Test Yourself 1 - Solutions.