AS-Level Maths | Differentiation

To differentiate
- multiply the coefficient by the power
- subtract one from the power
To work out the x-coordinate of a stationary point
- solve dy/dx = 0 for x
To work out the y-coordinate of a stationary point
- substitute x into the equation of your curve y = ...
To work out the nature of a stationary point
- substitute x into d²y/dx²
- If d²y/dx² < 0 then maximum
- If d²y/dx² > 0 then minimum
- If d²y/dx² = 0 then check the gradient on either side
To work out the gradient at a point on the curve
- substitute x into dy/dx
To work out when a function is increasing
- solve dy/dx > 0
To work out when a function is decreasing
- solve dy/dx < 0
To work out the equation of a tangent
- use dy/dx to get the gradient
- use equation of curve to get the y coodinate
- y = mx + c
To work out the equation of a normal
- use dy/dx to get the gradient
- take the negative reciprocal of the gradient
- use equation of curve to get the y coodinate
- y = mx + c