Derivative and its application

Derivative an its applications. Derivative, in mathematics, the rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and diff...

Antiderivatives

Antiderivtaives Antiderivatives are the opposite of derivatives. An antiderivative is a function that reverses what the derivative does. One function has many antiderivatives, but they all take the...

Differentials

Differentials:In calculus, the differential represents the principal part of the change in a function y = f(x) with respect to changes in the independent variable. The differential dy is defined b...

L Hospital's Rule

limx→4x2−16x−4limx→∞4x2−5x1−3x2limx→4⁡x2−16x−4limx→∞⁡4x2−5x1−3x2In the first limit if we plugged in x=4x=4 we would get 0/0 and in the second limit if we “plugged” in infinity we would get ∞/−∞∞/−∞...

Rolle's Theorem and Mean Value Theorem

Rolle's Theorem:If the function f(x) is1) continuous in the closed interval [a,b]2) differentiable in the open interval (a,b)3) f(a)=f(b)then there exists at least one point c belonging to (a,b) ...

Derivative of trigonometric function sinx and cosx

DERIVATIVE OF 'sinx'Let y=sinx…….iThen,Now,       Subtracting i from ii we get,By the first principle,DERIVATIVE OF 'cosx'Let y=cosx……. iThen,Now,       Subtracting i from ii we get,By the first pr...

Derivative of trigonometric function tanx and cotx

DERIVATE OF tanxLet y=tanx……. iThen,Now,       Subtracting i from ii we get,By the first principle,DERIVATE OF cotxLet y=cotx……. iThen,Now,       Subtracting i from ii we get,By the first principle,