Important Derivatives Formulas, Cheat Sheet of Pre-Calculus

Download Important Derivatives Formulas and more Cheat Sheet Pre-Calculus in PDF only on Docsity! Bright Career Science Academy Derivatives Formulas & Rules (Edition-3)       11 . . . . ( ) 1 c . (x ) c (x ) ( ) 0 df g . d f dx P ow er R ule w here P roduct R u le w here  " " is constant. Q uo tien t R u =le  • dx g n nn nd d d f d d f dg x n x f n f n R f g g f dx dx dx dx dx dx d dx d d d dc x f f c c dx dx dx dx dx dx                                         2 dg f. d 1 dfdx R ule for Square R oot f = . C hain R ule dx dx2 f • g dy dy du dx du dx             2 2 Derivativeof Trigonometric Functions d du sinu = cosu. dx dx d du cosu = sinu. dx dx d du tanu = sec u. dx dx d du cosec u = cosec u.cot u. dx dx d du secu =secu.tanu. dx dx d du cotu= cosec u. dx dx          2 2 Derivativeof HyperbolicFunctions d du sinhu = coshu. dx dx d du coshu =sinhu. dx dx d du tanhu =sech u. dx dx d du cosech u = cosech u.coth u. dx dx d du sechu = sechu.tanhu. dx dx d du cothu = cosech u. dx dx          1 2 1 2 1 2 1 2 1 2 1 2 Derivative of Inverse Trigonometric Functions d 1 du sin u = . dx dx1 u d 1 du cos u = . dx dx1 u d 1 du tan u = . dx 1+ u dx d 1 du cosec u =  . dx dxu u 1 d 1 du sec u = . dx dxu u 1 d 1 du cot u = . dx 1+ u dx                    1 2 1 2 1 2 1 2 1 2 1 2 Derivative of Inverse Hyperbolic Functions d 1 du sinh u= . dx dx1 + u d 1 du cosh u= . dx dxu 1 d 1 du tanh u= . dx 1 u dx d 1 du cosech u= . dx dxu 1+ u d 1 du sech u= . dx dxu 1 u d 1 du coth u= . dx 1 u dx                   u u u u a Derivativeof d du d du d 1 du d 1 du • e =e . • a =a . lna. • lnu= . • log u= . Exponential & Logarithmic Functions dx dx dx dx dx u dx dx u . lna dx n + 1 n n + 1 n ax ax f(x ) f(x ) 2 2 P o w er R u le o f In teg ra tio n x • x d x = n + 1 f • f . f d x = n + 1 f • d x = ln f f • a f(x ) d x = a f(x ) d x • 1 d x = x In teg ra tio n o f E x p o n en tia l F u n ctio n s e • e w h ere   d x = d (ax ) d x a • a d x = d ln a . f(x ) d x d x 1 • = t a + n 1 w h ere  n 1 x a                  1 1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 x an a d x x • =s in aa x d x • = ln x + x a x a x a x • a x d x = a x + s in 2 2 a x a x • x + a d x = x + a + s in h 2 2 a x a x • x a d x = x a co sh 2 2 a d x 1 a + x • = ln a x 2 a a x d x 1 x a • = ln x a 2 a x + a                                                      Integration of Trigonometric Functions cosax • sin ax dx= d (ax) dx sinax • cos ax dx= d (ax) dx ln sec ax ln cos ax • tan ax dx= = d d (ax) (ax) dx dx ln cosecax cot ax • cosec ax dx= d (ax) dx ln secax+tan ax • secax dx= d (ax) dx ln sin ax • cot ax dx=         2 2 d (ax) dx cotax • cosec ax dx= d (ax) dx tanax • sec ax dx= d (ax) dx cosec ax • cosecax.cot ax dx= d (ax) dx secax • sec ax. tan ax dx= d (ax :     )  “ ”     dx       .        Note Add Integration Constant c with Every Indefinite Integration Formula   Integration By Parts Rule Properties of D . . . . (x) (x) . (x) Property-1 ( efinite Integral Property-1 is Called "Fundamental theorem  ) of calcul s ) u ( ) ( ax ax b a d f g dx f g dx f g dx dx dx e a f f dx e f f x dx F b F a                      Property-2 ( ) ( ) Property-3 (x) (x) (x) Where " b a a b b c b a a c f x dx f x dx f dx f dx f dx a c b              Compiled By: Muzzammil Subhan M.Phil. Math (Minhaj University ) M.Sc. Math (Quaid-i-Azam University, Islamabad) M.Ed. (University of Sargodha), B.Sc., B.C.S. & PGD-IT Contact No: 0300-7779500 This page can also be Downloaded from Our Website WWW.MATHCITY.ORG Integration Formulas & Rules Compiled By: Muzzammil Subhan               2 2 2 2 2 3 3 2 2 3 3 3 2 2 2 2 A lgeb raic  F o rm u las 2 3 2 2 2 a b a b ab a b a b a b a b a b a b ab a b a b ab a b a b c a b c ab bc ca                               