Differentiation Formulas for Class 12 Chart and PDF

Differentiation Formulas For Class 12 Chart and PDF

Differentiation is the process of determining a function's derivative or rate of change. Check here the differentiation formulas of log x, cot x, tan x, sec x.

\frac{d}{d x} (\cos e c x) = - \cos e c x c o t x

Differentiation Definition

Differentiation is the process of determining a function’s derivative, or rate of change. In contrast to the abstract character of the theory that underpins it, differentiation can be accomplished using only algebraic manipulations, requiring only three basic derivatives, four rules of operation, and a working grasp of functions.

The three basic differentiation are:

(1) Algebraic functions –

D(xn) = nxn − 1

where n is any real number

(2) Trigonometric functions –

D(sin x) = cos x

D(cos x) = −sin x

(3) Exponential functions –

D(e^x) = e^x

The theory offers the following basic rules for differentiating the sum, product, or quotient of the any two functions f(x) and g(x) whose derivatives are known (where a and b are constants) for functions built up of combinations of these types of functions:

Differentiation Sum Rule

D(af + bg) = aDf + bDg

Differentiation Product Rule

D(fg) = fDg + gDf

Differentiation Quotient Rule

D(f/g) = (gDf − fDg)/g²

Differentiation Chain Rule

The chain rule is another basic rule that can be used to differentiate a composite function. If f(x) and g(x) are two functions, the composite function f(g(x)) is determined by first evaluating g(x) and then evaluating the function f at this g(x) value. The chain rule asserts that a product gives the derivative of a composite function:

D(f(g(x))) = Df(g(x)) ∙ Dg(x)

In other words, the first element on the right, Df(g(x)), indicates that the derivative of Df(x) is determined first as usual, and then x is replaced by the function g wherever it occurs (x).

Differentiation Formula

Differentiation is a fundamental concept in calculus that involves finding the derivative of a function with respect to its independent variable. Here are some differentiation formulas for common types of functions:

Differentiation Formula for Power Rule

If f(x) = x^n, where n is a constant, then the derivative f'(x) is given by:

f'(x) = n * x^(n-1)

Differentiation Formula for Constant Rule

If f(x) = c, where c is a constant, then the derivative f'(x) is:

f'(x) = 0

Differentiation Formula for Sum/Difference Rule

If f(x) = g(x) + h(x), then the derivative f'(x) is the sum of the derivatives of g(x) and h(x):

f'(x) = g'(x) + h'(x)

Differentiation Formula for Product Rule

If f(x) = g(x) * h(x), then the derivative f'(x) is given by:

f'(x) = g'(x) * h(x) + g(x) * h'(x)

Differentiation Formula for Quotient Rule

If f(x) = g(x) / h(x), then the derivative f'(x) is given by:

f'(x) = (g'(x) * h(x) – g(x) * h'(x)) / (h(x))^2

Differentiation Formula for Chain Rule

If y = f(g(x)), where y is a composite function of two functions f and g, then the derivative dy/dx is given by:

dy/dx = f'(g(x)) * g'(x)

Differentiation Formula for Exponential and Logarithmic Functions

- The derivative of e^x is e^x.
- The derivative of ln(x) is 1/x.
  
  Differentiation Formula for Trigonometric Functions
  - The derivative of sin(x) is cos(x).
  - The derivative of cos(x) is -sin(x).
  - The derivative of tan(x) is sec^2(x).

These are some of the basic differentiation formulas. There are additional rules and techniques for more complex functions. Remember that the rules of differentiation allow you to find the rate of change or slope of a function at any given point.

Differentiation Formula of sec x, tan x, cot x, Log x

Some of the most important and basic formulae of differentiation are:

If f(x) = xⁿ, in which n is any fraction or integer, then

f'(x) = nx^n-1

If f(x) = k, where k is a constant, then

f'(x) = 0

If f(x) = tan (x), then

f'(x) = sec²x

If f(x) = cos (x), then

f'(x) = -sin x

If f(x) = sin (x), then

f'(x) = cos x

If f(x) = ln(x), then

f'(x) = 1/x

If f(x) = e^x, then

f'(x) = e^x

Differentiation Formulas Chart Class 12

differentiation formulas chart class 12 is given below. Students of class 12 can easily learn all these differentiation formula for their board exams.

$\frac{d}{d x} (\sin x) = \cos x$

$\frac{d}{d x} (\cos x) = - \sin x$

$\frac{d}{d x} (\tan x) = s e c^{2} x$

$\frac{d}{d x} (c o t x) = - \cos e c^{2} x$

$\frac{d}{d x} (s e c x) = s e c x \tan x$

$\frac{d}{d x} (\cos e c x) = - \cos e c x c o t x$

$\frac{d}{d x} (\sin h x) = \cos h x$

$\frac{d}{d x} (\cos h) = \sin h x$

$\frac{d}{d x} (\tan h x) = s e c h^{2} x$

$\frac{d}{d x} (c o t x) = - \cos e c h^{2} x$

$\frac{d}{d x} (s e c h x) = - s e c h x \tan h x$

$\frac{d}{d x} (\cos e c h x) = - \cos e c x c o t h x$

Differentiation Formulas PDF for Class 12

Download the differentiation formula pdf from here.

Differentiation Formulas PDF

FAQs

What is differentiation used for?

In arithmetic, differentiation is used to calculate rates of change. The velocity, for example, is the rate of change of displacement (with respect to time) in mechanics. The acceleration is the rate of change of velocity (with respect to time).

How do u differentiate?

There are a few simple criteria that can be utilised to quickly distinguish between various functions. The derivative of y (with respect to x) is written dy/dx, pronounced "dee y by dee x" if y = some function of x (in other words, if y is equivalent to an expression including integers and x's).

What is differentiation in simple words?

Differentiation is the process of determining a function's derivative, or rate of change. In contrast to the abstract character of the theory that underpins it, differentiation can be accomplished using only algebraic manipulations, requiring only three basic derivatives, four rules of operation, and a working grasp of functions.