The differentiation of (\cos(x)) with respect to (x) is a fundamental concept in calculus. The derivative of (\cos(x)) is given by: \[\frac{d}{dx}(\cos(x)) = -\sin(x).\] This result is derived from the limit definition of the derivative and is a key part of the differentiation rules for trigonometric functions. The negative sine function, $-\sin(x)$, represents the rate […]

Number 54 is a composite number and we will find how to find the factors of 54. We will also see techniques to find out the Prime factorization of 54 easily Factors of 54 A factor of a number is an exact divisor of that number. So factors of 54 are the numbers which are

Number 40 is a composite number and we will find how to find the factors of 40. We will also see techniques to find out the Prime factorization of 40 easily Factors of 40 A factor of a number is an exact divisor of that number. So factors of 40 are the numbers which are

Number 56 is a composite number and we will find how to find the factors of 56. We will also see techniques to find out the Prime factorization of 56 easily Factors of 56 A factor of a number is an exact divisor of that number. So factors of 56 are the numbers which are

The integration of sec cube x $\sec ^3 x$, can be found using integration substitution and trigonometry identities . The integral of $\sec ^3 x$ with respect to (x) is: \[\int \sec^3 x \, dx =\frac {1}{2} \sec x \tan x +\frac {1}{2} \ln |sec x + tan x|+ C\] Here, (C) represents the constant

The integration of cos cube x $\cos ^3 x$, can be found using integration substitution and trigonometry identities . The integral of $\cos ^3 x$ with respect to (x) is: \[\int \cos^3 x \, dx =\frac {\sin 3x}{12} + \frac {3\sin x}{4} + C\] or \[\int \cos^3 x \, dx =-\frac{\sin^3(x)}{3} + \sin(x) + C\]

The integral of the exponential function , $e^x$, can be found using basic calculus principles. The integral of $e^x$ with respect to (x) is: \[\int e^x \, dx = e^x + C\] Here, (C) represents the constant of integration, which is added because the process of integration determines the antiderivative up to an arbitrary constant.

Integration of root a^2 +x^2, x^2 -a^2, a^2 -x^2 is given as $ \int \sqrt {a^2 – x^2} dx = \frac {1}{2} x \sqrt {a^2 – x^2} + \frac {1}{2} a^2 \sin^{-1} \frac {x}{a} + C$ $ \int \sqrt {a^2 + x^2} dx = \frac {1}{2} x \sqrt {a^2 + x^2} + \frac {1}{2} a^2