Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Calculus - Differentiation - Main page.

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

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).

 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.