Differentiation - 1

Introduction


2. Derivative from first principless

Definition of derivative
Lebnitz/s notation
Standard forms
Algebra of derivatives

Ch. 2 Differentiation - 3

Differentiability and continuity

Derivatives - 4

Derivatives of composite functions

If y = f(u) and u = g9x) then y = f[g(x)] is a composite function of x.

example y = u³ and u = 3x+4

y = (3x+4)³ is a composite function

Differentiation - 5

Derivatives of inverse functions

y = f(x)

x = g(y)

Differenentiation - 6

Logarithmic differentiation

y = [f(x)]^g(x)

take logarithms on both sides

log y = g(x) log [f(x)]
Differntiate

Ch. 2 Differentiation - 7

Differentiation of implicit functions

Ex: x² = y² + 2xy + 3x - 4y - 8 = 0

Ch. 2 Differentiation - 8

Differentiation of parametric functions

y is given as f(t) and x is given as g(t)

we have to find dy/dx
dy/dx = (dy/dt) *( dt/dx)