## Inverse Hyperbolic functions – Derivation formulas

Inverse Hyperbolic functions 1. ddxsinh-1x=11+x2 2. ddxcosh-1x=1x2-1 3. ddxtanh-1x=11-x2, |x|\lt1 4. ddxcoth-1x=1x2-1, |x|>1 5. ddxsech-1x=-1x1-x2, 0\ltx\lt1 6. ddxcosec h-1x=-1x1+x2, x>0 Example 1: Differentiate y=tanh-1(sinx) Solution: y'=11-sin2x·ddx(sinx) y'=11-sin2x·cosx y'=cosxcos2x y'=secx

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Hyperbolic functions $$1. \ \frac {d}{dx} \sin hx = \cos hx$$ $$2. \ \frac {d}{dx} \cos hx = \sin hx$$ $$3. \ \frac {d}{dx} \tan… Continue Reading Hyperbolic functions-Derivation formulas ## Inverse Trigonometric functions-Derivation formulas Inverse Trigonometric functions$$ 1. \ \frac {d}{dx} \sin^{-1}x = \frac {1}{\sqrt {1-x^2}}, \ -1 \lt x \lt 1  2. \ \frac {d}{dx} \cos^{-1}x = \frac {-1}{\sqrt {1-x^2}},…

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Trigonometric functions $$1. \ \frac {d}{dx} \sin x= \cos x$$ $$2. \ \frac {d}{dx} \cos x = - \sin x$$ $$3. \ \frac {d}{dx} \tan x… Continue Reading Trigonometric functions-Derivation formulas ## Derivative of Exponential Functions-Derivation formulas Derivative of Exponential Functions$$ 1. \ \frac {d}{dx} e^x = e^x  2. \ \frac {d}{dx} e^{f(x)} = e^{f(x)} \frac {d}{dx} f(x) 3. \ \frac {d}{dx} a^x…

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## Derivative of Logarithm Functions

Derivative of Logarithm Functions 1. ddxlnx=1x 2. ddxlogax=1xlna 3. ddxlnf(x)=1f(x)ddxf(x) 4. ddxlogaf(x)=1f(x)lnaddxf(x) Example: Differentiate g(t)=4log3t-lnt Solution: g'(t)=4tln(3)-1t

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## General derivative formula

General derivative formula 1. ddx(c)=0, where c is any constant. 1. \ \frac {d}{dx} (c)=0, \ where \ c \ is \ any \ constant. 2. ddxxn=nxn-1 2. \ \frac {d}{dx} x^n = nx^{n-1} 3. ddxx=1 3. \…

## Properties of derivative -derivative formulas

Properties of derivative Functions: f, g, y, u, v Argument (independent variable): x Real constant: k Angle: α 1. Derivative of a function: The derivative of a function y=f(x)…

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## Limits formula – Derivation formulas

Limits formula Limits math is very important in calculus. It is one of the basic prerequisites to understand other concepts in Calculus such as continuity, differentiation, integration limit formula, etc.…

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## Derivation formula

Introduction A derivation is a sequence of steps, logical or computational, from one result to another. The word derivation comes from the word "derive." "Derivation" can also refer to a…