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
Hyperbolic functions $$ 1. \ \frac {d}{dx} \sin hx = \cos hx $$ $$ 2. \ \frac {d}{dx} \cos hx = \sin hx $$ $$ 3. \ \frac {d}{dx} \tan…
Inverse Trigonometric functions $$ 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}},…
Trigonometric functions $$ 1. \ \frac {d}{dx} \sin x= \cos x$$ $$ 2. \ \frac {d}{dx} \cos x = - \sin x $$ $$ 3. \ \frac {d}{dx} \tan x…
Derivative of Exponential Functions $$ 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…
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
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 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)…
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.…
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…