Formulas Derivadas

Función Derivada Integral
y = c y’ = 0 c.xy = c.xy’ = c c.x2/2
y = xny’ = n.xn-1 xn+1/n+1
y = x-n y’ = -1/(n.xn-1)x-n+1/-n+1
y = x½ y’ = 1/(2.x½) 2.x3/2/3
y = xa/b y’ = a.x(a/b)-1/b x(a/b)+1/[(a/b)+1]
y = 1/x y’ = -1/x2 ln x
y = sen x y’ = cos x-cos x
y = cos x y’ = -sen x sen x
y = tg x y’ = 1/cos2x -ln cos x
y = cotg x y’ = -1/sen2x ln sen x
y = sec x y’ = senx/cos2x ln (tg ½.x)
y = cosec x y’ = -cos x/sen2x ln [cos x/(1 - sen x)]
y = arcsen x y’ = 1/(1 – x2)½ x.arcsen x + (1 – x2)½
y= arccos x y’ = -1/(1 – x2)½ x.arccos x – (1 – x2)½
y = arctg x y’ = 1/(1 + x2) x.arctg x – ½ln (1 + x2)
y = arccotg x y’ =-1/(1 + x2) x.arccotg x + ½ln (1 + x2)
y = arcsec x y’ = 1/[x.(x2 -1)½] 1
y = arccosec x y’ = -1/[x.(x2 – 1)½] 2
y = senh x y’= cosh x cosh x
y = cosh x y’ = senh x senh x
y = tgh x y’ = sech2x ln cosh x
y = cotgh x y’ = -cosech2x ln senh x
y = sechx y’ = -sech x.tgh x 3
y = cosech x y’ = -cosech x.cotgh x 4
y = ln x y’ = 1/x x.(ln x – 1)
y = logaxy’ = 1/x.ln a x.( logax– 1/ln a)
y = ex y’ = ex ex
y = axy’ = ax.ln a ax/ln a
y = xx y’ = xx.(ln x + 1) 5
y = euy’ = eu.u’ 6
y = u.vy’ = u’.v +v’.uu.dv + v.duy = u/v y’ = (u’.v – v’.u)/v2 7
y = uvy’ = uv.(v’.lnu + v.u’/u) 8
y = lnuvy’ = (v’.u.lnu – u’.v.lnv)/v.u.ln2u9