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Derivative Rules

December 10, 2020 by Prasanna

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.

 

Filed Under: Mathematics Tagged With: Chain rule, Derivative Rules, Differentiation of algebraic functions, Differentiation of hyperbolic functions, Differentiation of inverse trigonometrical functions, Differentiation of logarithmic and exponential functions, Differentiation of trigonometric functions, Product rule, Quotient rule, Scalar multiple rule, Standard Differentiation Formulae, Sum and difference rule

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