Here you will learn lagrange’s mean value theorem statement, its geometrical and physical interpretation with examples. Let’s begin – Lagrange’s Mean Value Theorem (LMVT) Statement : Let f be a function that satisfies the following conditions : (i) f is continuous in [a, b] (ii) f is differentiable in (a, b) Then there is a …
Here you will learn statement of rolle’s theorem, it’s geometrical and algebraic interpretation with examples. Let’s begin – Rolle’s Theorem Statement : Let f be a function that satisfies the following three conditions: (a) f is continous on the closed interval [a, b]. (b) f is differentiable on the open interval (a, b) (c) f(a) …
Here you will learn mean value theorems i.e rolle’s theorem, lagrange’s theorem and extreme value theorem. Let’s begin – Mean Value Theorems (a) Rolle’s Theorem Let f be a real valued function defined on the closed interval [a, b] such that (i) it is continuous on the closed interval [a, b], (ii) it is differentiable …
Here you will learn what is differentials errors and approximations with examples. Let’s begin – Differentials Errors and Approximations In order to calculate the approximate value of a function, differentials may be used where the differential of a function is equal to its derivative multiplied by the differential of the independent variable, In general dy …
Here you will learn derivative as a rate measure class 12 with examples. Let’s begin – Derivative as a Rate Measure Whenever one quantity y varies with another quantity x, satisfying some rule y = f(x), then \(dy\over dx\) (or f'(x)) represents the rate of change of y with respect to x and \(({dy\over dx})_{x=a}\) …
Here you will learn higher order derivatives of parametric equations with examples. Let’s begin – Higher Order Derivatives of Parametric Equations We know that the differentiation of parametric equations of type x = at and y = 2at is given by formula \(dy\over dx\) = \(dy/dt\over dx/dt\) where t is the parameter Now, by again …
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Here you will learn higher order derivatives of functions with examples. Let’s begin – Higher Order Derivatives Definition and Notations If y = f(x), then \(dy\over dx\), the derivative of y with respect to x, is itself, in general, a function of x and can be differentiated gain. To fix up the idea, we shall …
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Here you will learn differentiation of cosec inverse x or arccosecx x by using chain rule. Let’s begin – Differentiation of cosec inverse x or \(cosec^{-1}x\) : If x \(\in\) R – [-1, 1] . then the differentiation of \(cosec^{-1}x\) with respect to x is \(-1\over | x |\sqrt{x^2 – 1}\). i.e. \(d\over dx\) \(cosec^{-1}x\) …
Here you will learn differentiation of sec inverse x or arcsecx x by using chain rule. Let’s begin – Differentiation of sec inverse x or \(sec^{-1}x\) : If x \(\in\) R – [-1, 1] . then the differentiation of \(sec^{-1}x\) with respect to x is \(1\over | x |\sqrt{x^2 – 1}\). i.e. \(d\over dx\) \(sec^{-1}x\) …
Here you will learn differentiation of cot inverse x or arccotx x by using chain rule. Let’s begin – Differentiation of cot inverse x or \(cot^{-1}x\) : The differentiation of \(cot^{-1}x\) with respect to x is \(-1\over {1 + x^2}\). i.e. \(d\over dx\) \(cot^{-1}x\) = \(-1\over {1 + x^2}\). Proof using chain rule : Let …
