Here you will learn what is the differentiation of cotx and its proof by using first principle. Let’s begin – Differentiation of cotx The differentiation of cotx with respect to x is \(-cosec^2x\). i.e. \(d\over dx\) (cotx) = \(-cosec^2x\) Proof Using First Principle : Let f(x) = cot x. Then, f(x + h) = cot(x …
Here you will learn what is the differentiation of tanx and its proof by using first principle. Let’s begin – Differentiation of tanx The differentiation of tanx with respect to x is \(sec^2x\). i.e. \(d\over dx\) (tanx) = \(sec^2x\) Proof Using First Principle : Let f(x) = tan x. Then, f(x + h) = tan(x …
Here you will learn what is the differentiation of sinx and its proof by using first principle. Let’s begin – Differentiation of sinx The differentiation of sinx with respect to x is cosx. i.e. \(d\over dx\) (sinx) = cosx Proof Using First Principle : Let f(x) = sin x. Then, f(x + h) = sin(x …
Here you will learn what is the differentiation of cosx and its proof by using first principle. Let’s begin – Differentiation of cosx The differentiation of cosx with respect to x is -sinx. i.e. \(d\over dx\) (cosx) = -sinx Proof Using First Principle : Let f(x) = cos x. Then, f(x + h) = cos(x …
Here you will learn differentiation of determinant with example. Let’s begin – Differentiation of Determinant To differentiate a determinant, we differerentiate one row (or column) at a time, keeping others unchanged. for example, if D(x) = \(\begin{vmatrix} f(x) & g(x) \\ u(x) & v(x) \end{vmatrix}\) , then \(d\over dx\){D(x)} = \(\begin{vmatrix} f'(x) & g'(x) \\ …
Here you will learn differentiation of parametric functions with example. Let’s begin – Differentiation of Parametric Functions Sometimes x and y are given as functions of a single variable e.g. x = \(\phi\)(t), y = \(\psi\)(t) are two functions of a single variable. In such a case x and y are called parametric functions or …
Here you will learn what is differentiation of infinite series class 12 with examples. Let’s begin – Differentiation of Infinite Series Sometimes the value of y is given as an infinite series and we are asked to find \(dy\over dx\). In such cases we use the fact that if a term is deleted from a …
Here you will learn formula of logarithmic differentiation with examples. Let’s begin – Logarithmic Differentiation We have learnt about the derivatives of the functions of the form \([f(x)]^n\) , \(n^{f(x))}\) and \(n^n\) , where f(x) is a function of x and n is a constant. In this section, we will be mainly discussing derivatives of …
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Here you will learn what is the differentiation of implicit function with examples. Let’s begin – Differentiation of Implicit Function If the variables x and y are connected by a relation of the form f(x,y) = 0 and it is not possible or convenient to express y as a function x in the form y …
Here you will learn what is the differentiation of inverse trigonometric functions with examples. Let’s begin – Differentiation of Inverse Trigonometric Functions (i) If x \(\in\) (-1, 1), then the differentiation of \(sin^{-1}x\) or arcsinx with respect to x is \(1\over \sqrt{1-x^2}\). i.e. \(d\over dx\) \(sin^{-1}x\) = \(1\over \sqrt{1-x^2}\) , for x \(\in\) (-1, 1). …
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