# C1 Differentiation Notes - (AQA) Maths As Level

Notes and expalnations

Teacher recommended

- Created by: unknown
- Created on: 17-11-11 21:42

First 365 words of the document:

Differentiation

This is used to find the gradient of a curve at different points. It also helps us find the equation of a

tangent or a normal to a curve, stationary points on a curve, minimum and maximum points and tells

us whether a function is increasing or decreasing

Times by the power, then take one away from the power

Example: x5 becomes 5x4

Example: 3x becomes 3

Rule: x becomes 1

Rule: 6 becomes 0

If they give you the gradient and the equation, simply find x by putting it equal to the

derivative and then sub in your x value into the original equation

Use different letters instead of dx/dy

Remember to add the units at the end

Always expand and simplify before differentiating and cancel

afterwards

Rates of change

They will give you an equation (something = something else)

1. Differentiate it as you would a normal equation/function

2. They will also give you a value to sub into your derivative (this is like the `x' value in an

equation)

The key is to treat it like an equation, but don't forget the units (may need to figure out the units

according to the variables they have given you eg cm per second OR cm-1)

Equation of a tangent to the curve

The Tangent to the curve Touches the curve

The tangent is a straight line (therefore, all the

straight line rules and equations apply to it)

The gradient of the point where the curve and tangent touch is the same

To find the equation of a tangent when they give you the equation of the curve and the x coordinate:

1. Differentiate equation of the curve (so you can find dy/dx or the gradient)

2. Sub in your x value, to find your gradient

3. Go back to your original equation, sub in your x value, then find y

4. Use your x value and y value (your coordinates) to find the equation of the tangent using y

- y1 = m(x - x1)

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