Trigonometry, Derivation, Intregration, Set

Trigonometry, Derivation, Intregration, Set

Sigma Notation:-

Pi Notation:-

Intersection Notation:-

Union Notation:-

Trigonometry

Set

Derivation

if x is real number. then,

if f(-x)=f(x) then f(x) even function; when f(-x)= - f(x) then f(x) odd function

{\frac {d}{dx}}e^{x}=e^{x}.

{\frac {d}{dx}}a^{x}=a^{x}\ln(a).

{\frac {d}{dx}}\ln(x)={\frac {1}{x}},\qquad x>0.

{\frac {d}{dx}}\log _{a}(x)={\frac {1}{x\ln(a)}}.

{\frac {d}{dx}}\sin(x)=\cos(x).

{\frac {d}{dx}}\cos(x)=-\sin(x).

{\frac {d}{dx}}\tan(x)=\sec ^{2}(x)={\frac {1}{\cos ^{2}(x)}}=1+\tan ^{2}(x).

{\frac {d}{dx}}\arcsin(x)={\frac {1}{\sqrt {1-x^{2}}}},-1<x<1.

{\frac {d}{dx}}\arccos(x)=-{\frac {1}{\sqrt {1-x^{2}}}},-1<x<1.

{\frac {d}{dx}}\arctan(x)={\frac {1}{1+x^{2}}}

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if y=f(u) and u=ɸ(x) , then dy/dx=dy/du . du/dx

if y=f(t) and x=g(t),then

$integration$

Important

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