Derivative Rules

Derivative Rules

The rate of change of one quantity with respect to some another quantity has a great importance.
The rate of change of a quantity ‘y’ with respect to another quantity ‘x’ is called the derivative or differential coefficient of y with respect to x.

Derivative Rules 1

The Derivative means the slope of a function at any point.

Some Standard Differentiation Formulae

(1) Differentiation of some common functions:
Derivative Rules 2
(2) Differentiation of algebraic functions:
In particular
Derivative Rules 3
(3) Differentiation of trigonometric functions:
Derivative Rules 4
(4) Differentiation of logarithmic and exponential functions:
Derivative Rules 5
(5) Differentiation of inverse trigonometrical functions:
Derivative Rules 6
(6) Differentiation of hyperbolic functions:
Derivative Rules 7
(7) Suitable substitutions
Derivative Rules 8

Rules for Differentiation

Let f(x), g(x) and u(x) be differentiable functions

  1. If at all points of a certain interval, f'(x) = o, then the function f(x) has a constant value within this interval.
  2. Chain rule
    (i) Case I: if y is a function of u and u is a function of x, then derivative of y with respect to x is
    Derivative Rules 9
    (ii) Case II: If y and x both are expressed in terms of t, y and x both are differentiable with respect to t, then
    Derivative Rules 10
  3. Sum and difference rule: Using linear property
    Derivative Rules 11
  4. Product rule
    Derivative Rules 12
  5. Scalar multiple rule:
    Derivative Rules 13
  6. Quotient rule:
    Derivative Rules 14
    Provided g≠0.

 

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