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About Differentiation and Integration Formula

Differential Calculus Formulas

Differentiation is the process of determining a function's derivative. The derivative of a function is defined as y = f(x) of a variable x, which is the rate of change of variable y concerning variable x. It denotes a function's derivative concerning the variable x. There are several rules for determining a function's derivative. These rules simplify the differentiation process for a variety of functions, including trigonometric and logarithmic functions. The following is a list of differential calculus formulas:

$\frac{d}{dx} k = 0$
$\frac{d}{dx} [f (x) \pm g (x)] = f' (x) \pm g' (x)$
$\frac{d}{dx} [k . f (x) = k . f' (x)]$
$\frac{d}{dx} [f (x) . g (x)] = f (x) g' (x) + g (x) f' (x)$
$\frac{d}{dx} (\frac{f (x)}{g (x)}) = \frac{g (x) f' (x) - f (x) g' (x)}{{[g (x)]}^{2}}$
$\frac{d}{dx} f (g (x)) = f' (g (x)) . g' (x)$
$\frac{d}{dx} x^{n} = {nx}^{n - 1}$
$\frac{d}{dx} \sin x = \cos x$
$\frac{d}{dx} \cos x = - \sin x$
$\frac{d}{dx} \tan x = \sec^{2} x$
$\frac{d}{dx} \cot x = - \csc^{2} x$
$\frac{d}{dx} \sec x = \sec x \tan x$
$\frac{d}{dx} \csc x = - \csc x \cot x$
$\frac{d}{dx} e^{x} = e^{x}$
$\frac{d}{dx} a^{x} = a^{x} \ln a$
$\frac{d}{dx} \ln |x| = \frac{1}{x}$
$\frac{d}{dx} \sin^{- 1} x = \frac{1}{\sqrt{1 - x^{2}}}$
$\frac{d}{dx} \cos^{- 1} x = \frac{- 1}{\sqrt{1 - x^{2}}}$
$\frac{d}{dx} \tan^{- 1} x = \frac{1}{x^{2} + 1}$
$\frac{d}{dx} \cot^{- 1} x = \frac{- 1}{x^{2} + 1}$
$\frac{d}{dx} \sec^{- 1} x = \frac{1}{|x| \sqrt{x^{2} - 1}}$
$\frac{d}{dx} \csc^{- 1} x = \frac{- 1}{|x| \sqrt{x^{2} - 1}}$

All Integral Calculus Formulas

The most fundamental application of integration is to combine the slices into a whole. In other terms, integration is the process of continuous addition, and the constant of integration is represented by the variable "C." However, integration formulas are frequently employed to discover the most significant things' central points, areas, and volumes. It also aids in determining the area under a function's curve. There are a few key integral calculus formulas that aid in the solution process. These integral calculus formulas aid in reducing the amount of time required to solve the problem. The following is a list of integral calculus formulas: More Maths Formulas on the parent's page.

$\int d x = x + C$
$\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C$
$\int \frac{d x}{x} = \ln | x | + C$
$\int e^{x} d x = e^{x} + C$
$\int a^{x} d x = \frac{1}{\ln a} a^{x} + C$
$\int \ln x d x = x \ln x - x + C$
$\int \sin x d x = - \cos x + C$
$\int \cos x d x = \sin x + C$
$\int \tan x d x = - \ln | \cos x | + C$
$\int c o t x d x = \ln | \sin x | + C$
$\int s e c x d x = \ln | s e c x + \tan x | + C$
$\int c s c x d x = - \ln | c s c x + c o t x | + C$
$\int s e c^{2} x d x = \tan x + C$
$\int c s c^{2} x d x = - c o t x + C$
$\int s e c x \tan x d x = s e c x + C$
$\int c s c x c o t x d x = - c s c x + C$
$\int \frac{d x}{\sqrt{a^{2} - x^{2}}} = \sin^{- 1} \frac{x}{a} + C$
$\int \frac{d x}{a^{2} + x^{2}} = \frac{1}{a} \tan^{- 1} \frac{x}{a} + C$
$\int \frac{d x}{x \sqrt{x^{2} - a^{2}}} = \frac{1}{a} s e c^{- 1} \frac{|x|}{a} + C$

Differentiation and Integration Formula

About Differentiation and Integration Formula

Differential Calculus Formulas

All Integral Calculus Formulas

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