## Differentiation

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### D1 Limit of a function

The limit of a function means finding the value of a curve at a particular point. But what is that point? A value to many decimal places can be very long, to define a value that is very precise. The...

### D10 Rates of change

If there is a relationship between two or more variables (like, area and radius of a circle (A = πr2 ), or pressure, volume and temperature of a gas), then there will also be a relationship between...

### D11 Small changes and approximations

Sometimes a small change in one variable can render a big change in a larger value. For example, a small increase (or error) in the radius of a sphere means a lot more volume is added! If you...

### D12 Implicit differentiation

What is implicit differentiation? How do you differentiate a function (say y=) that has two different variables in it (say x and k)? What do you do when you cannot express one as a function of the...

### D13 Partial differentiation

What is partial differentiation? You may have an expression with 3 variables or more. The volume (V) of a cylinder for example depends on radius(r.) and height(h). It makes it easier to hold one...

### D14 Higher Order Derivatives

Higher derivatives are used in many mathematical, scientific and engineering subjects.

### D2 Gradients, tangents and derivatives

A tangent is a line that touches a curve at only one point. Where that point sits along the function curve, determines the slope (i.e. the gradient) of the tangent to that point.

### D3 Differentiation from first principles

Learn how to take a derivative of a function using first principles. Using this method is the best way to understand the concepts around differentiation.

### D4 Rules for differentiation

Learn about the rules for differentiation and the different notations that are used.

### D5 The chain rule

How do you differentiate a larger function that has components that are smaller functions? This module will show you how to package these functions and work them out separately, before plugging them...

### D6 The product rule

What is the product rule? It is useful when you want to differentiate a function that comprises one function multiplied by another function.

### D7 The quotient rule

What is the quotient rule? The quotient rule is like the product rule but this time it is for one function that is divided by another (rather than multiplied).

### D8 Maxima and minima

How do you find the maximum (highest) or minimum (lowest) value of a curve? The maximum or minimum values of a function occur where the derivative is zero. That is where the graph of the function has...

### D9 Curve sketching

If you find some key points of a function such as: maxima, minima, or turning points; x and y axis intercepts; and regions where the gradient is positive or negative, you can put together a sketch of...

### Differentiation

Watch these videos on differentiation in mathematical functions to develop your maths skills in this area.