# Differentiation

## Differentiation of sec inverse 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. $$d\over dx$$ $$sec^{-1}x$$ …

## Differentiation of cot inverse 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 …

## Differentiation of tan inverse x

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 …

## Differentiation of Exponential Function

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 + …

## Differentiation of cosecx

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 …