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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Here you will learn what is chain rule in differentiation with examples. Let’s begin – Chain Rule in Differentiation If f(x) and g(x) are differentiable functions, then fog is also differentiable and (fog)'(x) = f'(x) = f'(g(x)) g'(x) or, \(d\over dx\) {(fog) (x)} = \(d\over d g(x)\) {(fog) (x)} \(d\over dx\) (g(x)). Remark 1 : The …
Here you will learn what is quotient rule in differentiation with examples. Let’s begin – Quotient Rule in Differentiation If f(x) and g(x) are two differentiable functions and g(x) \(\ne\) 0, then \(d\over dx\) {\(f(x)\over g(x)\)} = \({g(x) {d\over dx} (f(x)) – f(x) {d\over dx} (g(x))}\over {(g(x))^2}\) Example 1 : find the differentiation of \(sinx\over …
Here you will learn what is product rule in differentiation with examples. Let’s begin – Product Rule in Differentiation If f(x) and g(x) are differentiable functions, then f(x)g(x) is also differentiable function such that \(d\over dx\) {f(x) g(x)} = \(d\over dx\) (f(x)) g(x) + f(x). \(d\over dx\) (g(x)) If f(x), g(x) and h(x) are differentiable …
