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
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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
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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
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Here you will learn what is derivative or differentiation and various differentiation formulas class 12. Let’s begin – What is Derivative or Differentiation ? Let f(x) be a differentiable or derivable function on [a, b]. Then, \(lim_{h \to 0}\) \(f(x + h) – f(x)\over h\) or, \(lim_{h \to 0}\) \(f(x – h) – f(x)\over -h\)
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