Here you will learn the differentiation of constant function proof and examples. Let’s begin – Differentiation of Constant The differentiation of constant function is zero. i.e. \(d\over dx\)(c) = 0. Proof : Let f(x) = c, be a constant function. Then, By using first principle, \(d\over dx\) (f(x)) = \(\displaystyle{\lim_{h \to 0}}\) \(f(x + h) …
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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 …
Here you will learn differentiation of tan inverse x or arctanx x by using chain rule. Let’s begin – Differentiation of tan inverse x or \(tan^{-1}x\) : The differentiation of \(tan^{-1}x\) with respect to x is \(1\over {1 + x^2}\). i.e. \(d\over dx\) \(tan^{-1}x\) = \(1\over {1 + x^2}\). Proof using chain rule : Let …
Here you will learn differentiation of cos inverse x or arccos x by using chain rule. Let’s begin – Differentiation of cos inverse x or \(cos^{-1}x\) : If x \(\in\) (-1, 1) , then the differentiation of \(cos^{-1}x\) with respect to x is \(-1\over \sqrt{1 – x^2}\). i.e. \(d\over dx\) \(cos^{-1}x\) = \(-1\over \sqrt{1 – …
Here you will learn differentiation of sin inverse x or arcsin x by using chain rule. Let’s begin – Differentiation of sin inverse x or \(sin^{-1}x\) : If x \(\in\) (-1, 1) , then the differentiation of \(sin^{-1}x\) with respect to x is \(1\over \sqrt{1 – x^2}\). i.e. \(d\over dx\) \(sin^{-1}x\) = \(1\over \sqrt{1 – …
Here you will learn differentiation of log x i.e logarithmic function by using first principle and its examples. Let’s begin – Differentiation of log x (Logarithmic Function) with base e and a (1) Differentiation of log x or \(log_e x\): The differentiation of \(log_e x\), x > 0 with respect to x is \(1\over x\). …
Here you will learn differentiation of exponential function by using first principle and its examples. Let’s begin – Differentiation of Exponential Function (1) Differentiation of \(e^x\) : The differentiation of \(e^x\) with respect to x is \(e^x\). i.e. \(d\over dx\) \(e^x\) = \(e^x\) Proof Using first Principle : Let f(x) = \(e^x\). Then, f(x + …
Here you will learn what is the differentiation of cosecx and its proof by using first principle. Let’s begin – Differentiation of cosecx The differentiation of cosecx with respect to x is -cosecx.cotx i.e. \(d\over dx\) (cosecx) = -cosecx.cotx Proof Using First Principle : Let f(x) = cosec x. Then, f(x + h) = cosec(x …
