Bsc Maths Derivative Formula

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Some Important Derivative

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d d n c=0 where c is constant · x = nx n -1 dx dx ì d d d · tan x = sec2 x · csc x = - csc x cot x ïï · dx sin x = cos x dx dx í d d ï · d cos x = - sin x · cot x = - csc2 x · sec x = sec x tan x ïî dx dx dx ì d 1 d 1 d 1 -1 Sin -1x = · Sec -1 x = ï· · Tan x = 2 2 dx 1- x ï dx x x 2 -1 dx 1+ x í d -1 d -1 ï· d Cos -1 x = -1 · Csc -1x = · Cot -1x = 2 2 ï dx dx dx 1+ x 1- x x x2 -1 î d 1 ì d x x · log a x = ïï· dx a = a ln a dx x ln a í d 1 ï· d e x = e x · ln x = ïî dx dx x ì d d d · tanh x = sech 2 x · sech x = - sech x tanh x ïï· dx sinh x = cosh x dx dx í d d ï· d cosh x = sinh x · coth x = - csch 2 x · csch x = - csch x coth x ïî dx dx dx ì d 1 d -1 d 1 -1 Sinh-1x = · Sech -1 x = ï· · Tanh x = dx x2 + 1 ï dx x 1 - x2 dx 1 - x2 í d 1 d -1 ï· d Cosh -1 x = 1 · Coth -1 x = · Csch-1x = 2 ï dx dx dx 1- x x 2 -1 x 1 + x2 î ·

Some Standard nth Derivative m -n dn m! m a n ( ax + b ) if m ³ n · n (ax + b) = dx ( m - n )!

n d n æ 1 ö ( -1) n! a · = dx n çè ax + b ÷ø (ax + b)n +1 n

(-1)n -1 ( n - 1)! a n dn ax dn é ù ln( ax + b ) = · = a n ea x n ë n n e û dx dx (ax + b) n n d æ pö d æ pö n n · · ÷ n sin( ax + b) = a sin ç ax + b + n . n cos(ax + b) = a cos ç ax + b + n . dx 2ø dx 2 ÷ø è è n æ d n ax 2 2 2 ax -1 b ö · n e sin(bx + c) = ( a + b ) e sin ç bx + c + n tan dx a ÷ø è ·

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n æ d n ax bö 2 2 2 ax e cos( bx + c ) = ( a + b ) e cos ç bx + c + n tan -1 ÷ n dx aø è

Leibniz’s Theorem dn uv) = nC0 u ( n )v + nC1 u ( n -1)v¢ + nC2 u ( n -2)v¢¢ + ×××××××××××××× + n Cn-1 u¢v n -1 + nCn u v n n( dx Made by Atiq ur Rehman ( [email protected] ) http://www.mathcity.org Submit errors at http://www.mathcity.org/error