DIFFERENTION
Is the Process of finding derivative
Is used to determine the rate of change with respect to time.
ds/dt=v then dv/dt=a
it also allows to find the rate of change of y with respect to x which on a graph of y
against x is the gradient of the curve.
dy/dx = y2-y1/x2-x1 =gradient of the graph
note that dy/dx is the derivative of y with respect to x
DIFFERENTIATION FROM THE FIRST PRINCIPLE
Consider the function f(x) that depend on a variable x
F(x)=3x2 then f(x)=6x
DIFFERENTIAL TABLE
y dy/dx
constant 0
Sin x Cos x
Cos x -sin x
ex ex
ekx K ekx
Tan x Sec2x
In |x| 1/x
Sin ax a cos ax
Cos ax -a sinax
METHODS OF DIFFERENTIATION
1. Chain rule
2. Product rule
3. Quotient rule
CHAIN RULE
Is a special rule of differentiating the function of another function.
Is the Process of finding derivative
Is used to determine the rate of change with respect to time.
ds/dt=v then dv/dt=a
it also allows to find the rate of change of y with respect to x which on a graph of y
against x is the gradient of the curve.
dy/dx = y2-y1/x2-x1 =gradient of the graph
note that dy/dx is the derivative of y with respect to x
DIFFERENTIATION FROM THE FIRST PRINCIPLE
Consider the function f(x) that depend on a variable x
F(x)=3x2 then f(x)=6x
DIFFERENTIAL TABLE
y dy/dx
constant 0
Sin x Cos x
Cos x -sin x
ex ex
ekx K ekx
Tan x Sec2x
In |x| 1/x
Sin ax a cos ax
Cos ax -a sinax
METHODS OF DIFFERENTIATION
1. Chain rule
2. Product rule
3. Quotient rule
CHAIN RULE
Is a special rule of differentiating the function of another function.
