Tangents and Normals The equation of a tangent and normal takes the form of a straight line i.e. To find the equation you need to find a value for x, y and m and then substitute to find the value of c.
Find the equation of the tangent to the curve y = x2 – 3x + 18 at the point (1, 16). x = 1 y = 16 Substituting
To find the equation of the normal, use the perpendicular gradient i.e.
Worksheet 2
Rules of Differentiation Differentiating Trig Functions
A list of the trigonometry differentials is given in your formula sheet.
Exponential
Chain Rule applies when we have a function of a function e. g Chain Rule applies when we have a function of a function e.g. Take two functions: Now combine them into one function by eliminating u Function 1 Function 2
Chain Rule applies when we have a function of a function e. g Chain Rule applies when we have a function of a function e.g. Take two functions: Note: Function 1 Function 2
Think of it like this: Differentiate the first function as a whole and then differentiate what is inside of it.
Differentiate function 1 Think of it like this: Differentiate the first function as a whole... Differentiate function 1
Think of it like this: Differentiate the first function as a whole and then differentiate what is inside of it. Then function 2
Example: Function 1 Function 2 Differential of 2x + 4 Differential of sin
Differentiating logs Note: You can only differentiate natural log so any other base needs to be converted first.
Examples
Hard Example 1 4 3 2 4 1 3 2
Product Rule
Product Rule f g
Product Rule
Product Rule
Quotient Rule
Quotient Rule f g
Quotient Rule
Quotient Rule
Quotient Rule
Quotient Rule
Quotient Rule
When a curve is written in the form it is said to be defined explicitly. When a curve is written in the form it is said to be defined implicitly. Example:
Implicit differentiation Differentiating with respect to x
Implicit differentiation Differentiating with respect to x
Implicit differentiation Differentiating with respect to x
Implicit differentiation
Implicit differentiation
Parametric Equations
Parametric Equations
Parametric Equations
Parametric Equations
Example 2
Second derivative
Second derivative
Second derivative
Example 2