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Differentiation Formulas For Classes 11 and 12

 Differentiation For Classes 11 & 12

Differentiation formulas and basic concepts for classes 11 and 12 strictly according to the CBSE syllabus. Basic formulas of calculus

Differentiation formulas

DERIVATIVE BY FIRST PRINCIPAL

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 DIFFERENTIATION OF SOME IMPORTANT  FUNCTIONS

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DIFFERENTIATION OF SOME TRIGONOMETRIC FUNCTIONS

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PRODUCT RULE OF DIFFERENTIATION

  (uv)' = u'v + uv'   OR

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Example : Differentiate y = x2sinx, w.r.t. x
Solution

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QUOTIENT RULE OF DIFFERENTIATION


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Example: Differentiate   equation , w. r. t. x
Solution: 

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Chain Rule of finding the differentiations

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Example: Differentiate f(x) = (sin3x)4  with respect to x
Solution: f(x) = (sin3x)4 

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CONCEPT OF DIFFERENTIABILITY

A function is formally considered differentiable if its derivative exists at each point in its domain.
For a function to be differentiable it nust be continuous.

DEFINITION OF DIFFERENTIABILITY
f(x) is said to be differentiable at the point x = a if the derivative f ‘(a) exists at every point in its domain. It is given by

equation 
This formula is derived from Lagranges Mean Value Theorem.
Putting  x = a + h, as x → a, h → 0 so this can be written as 

equation 

CALCULATING DIFFERENTIABILITY
For checking the differentiability of a function we have to calculate Left Hand Differentiability (LHD) and Right Hand Differentiability (RHD)

It is batter to use basic formula of finding the differentiability as given below

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If LHD = RHD then the function is differentiable

Note: If a function is differentiable at any point, it is necessarily continuous at that point.

Example: Examine the function  equation   for differentiability at x = 2.
Solution: 
At x < 2, f(x) = 1 + x

equation 

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At x > 2 f(x) = 5 - x

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⇒ At x = 2, Lf ' (2) ≠ Rf ' (2)

⇒ LHD  ≠ RHD

⇒ f(x) is not differentiable at x = 2

DIFFERENTIATION OF INVERSE TRIGONOMETRIC FUNCTIONS
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THANKS FOR YOUR VISIT
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