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Differentiation formula

Fomulae of Differentiation d⁄dx (c) = 0   Where c is constant.d⁄dx (cx) = c   Where c is constant.du⁄dt = du⁄dx ⋅ dx⁄dtd⁄dx (u+v) = du⁄dx + dv⁄dxd⁄dx (uv) = u dv⁄dx + v du⁄dxd⁄dx ( xn ) = n xn-1  Where n is real number.d⁄dx un = n un-1du⁄dx   Where u is function of x.d⁄dx sin x = cos x d⁄dx cos x = -sin x d⁄dx tan x = sec2 x d⁄dx cot x = - cosec2 x d⁄dx sec x = tan x sec x d⁄dx cosec x = - cot x cosec x d⁄dx loge x = 1⁄xd⁄dx loge u = 1⁄udu⁄dxd⁄dx ( ex ) = exd⁄dx ( eax ) = a eaxd⁄dx sin ax = a cos ax d⁄dx sin (ax+b) = a cos (ax+b) d⁄dx cos ax = - a sin ax d⁄dx cos (ax+b) = - a sin (ax+b)

How many elements are there in the periodic table?

There are 118 chemical elements in the periodic table. List of all chemical elements is given below. Elements of periodic tableAtomic numberElement SymbolElement Name1 HHydrogen2HeHelium3LiLithium4BeBeryllium5BBoron6CCarbon7NNitrogen8OOxygen9FFluorine10NeNeon11NaSodium12MgMagnesium13AlAluminium14SiSilicon15PPhosphorus16SSulfur17ClChlorine18ArArgon19KPotassium20CaCalcium21ScScandium22TiTitanium23VVanadium24CrChromium25MnManganese26FeIron27CoCobalt28NiNickel29CuCopper30ZnZinc31GaGallium32GeGermanium33AsArsenic34SeSelenium35BrBromine36KrKrypton37RbRubidium38SrStrontium39YYttrium40ZrZirconium41NbNiobium42MoMolybdenum43TcTechnetium44RuRuthenium45RhRhodium46Pd Palladium 47 AgSilver48CdCadmium49InIndium50SnTin51SbAntimony52TeTellurium53IIodine54XeXenon55CsCaesium56BaBarium57LaLanthanum58CeCerium59PrPraseodymium60NdNeodymium61PmPromethium62SmSamarium63EuEuropium64GdGadolinium65TbTerbium66DyDysprosium67HoHolmium68ErErbium69TmThulium70YbYtterbium71LuLutetium72HfHafnium73TaTantalum74WTungsten75R…

Integration formula

Integration formula

∫ xn dx = xn+1⁄n+1   where ( n≠ -1 )

∫ dx = x

∫ c xn dx = c xn+1⁄n+1   where ( n≠ -1 )

∫ 1⁄x dx = ln x

∫ sin x dx = - cos x

∫ cos x dx = sin x

∫ ex dx = ex

∫ ( u+v ) dx = ∫ u dx + ∫ v dx

∫ sec2 x dx = tan x

∫ cosec2 x dx = - cot x

∫ sec x tan x dx = sec x

∫ cosec x cot x dx = - cosec x

∫ eax dx = 1⁄a eax

∫ sin ax dx = - 1⁄a cos ax

∫ sin (ax+b) dx = - 1⁄a cos (ax+b)

∫ cos ax dx = 1⁄a sin ax

∫ cos (ax+b) dx = 1⁄a sin (ax+b)

Trigonometry formula

Basic trigonometry formula

Perp./Hyp. = sin θ
Base/Hyp. = cos θ
Perp./Base = tan θ
Base/Perp. = cot θ
Hyp./Base = sec θ
Hyp./Perp. = cosec θ

Baudhayana formula
( Hyp. )2 = ( Base )2 + ( Perp.)2
Some common trigonometric Formulas

sin(A+B) = sin A cos B + cos A sin B
sin(A-B) = sin A cos B - cos A sin B
cos(A+B) = cos A cos B - sin A sin B
cos(A-B) = cos A cos B + sin A sin B

sin 2A = 2 sin A cos B
cos 2A = cos2 A - sin2 A
cos 2A = 1 - 2 sin2 A
sin(A+B) + sin(A-B) = 2 sin A cos B
sin(A+B) - sin(A-B) = 2 cos A sin B
cos(A+B) + cos(A-B) = 2 cos A cos B
cos(A+B) - cos(A-B) = -2 sin A sin B

Trigonometric Ratios
Trigonometry ratio table:
Table of trigonometrical ratios of some standard angels:




Angle


sin θ


cos θ


tan θ




00


0


1


0




300


$$\frac{1}{2}$$


$$\frac{\sqrt{3}}{2}$$


$$\frac{1}{\sqrt{3}}$$




450


$$\frac{1}{\sqrt{2}}$$


$$\frac{1}{\sqrt{2}}$$


1




600


$$\frac{\sqrt{3}}{2}$$


$$\frac{1}{2}$$


$$\sqrt{3}$$




900


1


0


$$\infty $$




1200


$$\frac{\sqrt{3}}{2}$$


$$-\frac{1}{2}$$


$$-\sqrt{3}$$




1350


$$\frac{1}{\sqrt{2}}$$


$$-\frac{1}{\sqrt{2…