C1 Differentiation Notes - (AQA) Maths As Level

Notes and expalnations

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  • Created on: 17-11-11 21:42
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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
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
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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Equation of a normal to the curve
The normal to curve is always at a right angle to
the tangent
This means that it's perpendicular to the tangent
This means that the product of the gradients is -1
m1 x m2 = -1
To find the equation of a normal when you are given the equation of a curve and an x coordinate:
1. You find the gradient of the tangent first
2.…read more

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Increasing and decreasing functions
If the gradient of a function is POSITIVE then it is INCREASING
If the gradient of a function is NEGATIVE then it is DECREASING
1. Differentiate and sub in your x value
2.…read more

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A good set of revision notes (printed with illustrations) on differentiation.(Core 1)

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