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 \(1\over x\). …
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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 …
Here you will learn what is the differentiation of secx and its proof by using first principle. Let’s begin – Differentiation of secx The differentiation of secx with respect to x is secx.tanx i.e. \(d\over dx\) (secx) = secx.tanx Proof Using First Principle : Let f(x) = sec x. Then, f(x + h) = sec(x …
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 …
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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 …
