TABLA DE DERIVADAS.

FUNCIÓN SIMPLE

FUNCIÓN COMPUESTA

y= K

y´= 0

y = x

y´= 1

y = xn        

y´= n xn -1

y = (f(x))n        

y´= n (f(x))n -1f´(x)

y =[pic 1]

y ´=  [pic 2]

y = [pic 3]

y ´= [pic 4]

y = [pic 5]

y´=[pic 6]

y= [pic 7] 

y´=[pic 8]

y = e x

y´= e x

y = ef(x)

y´= ef(x)·f´(x)

y = a x

y´= a x lna

y = af(x)

y´= af(x)·lna·f´(x)

y= lnx

y´= [pic 9]

y = ln f(x)

y´= [pic 10]

y = log ax

y´= [pic 11]logae

y = loga f(x)

y´=  [pic 12] 

y = sen x

y´= cos x

y = sen f(x)

y´= cos f(x) f´(x)

y = cos x        

y´= - senx

y = cos f(x)

y´= -sen f(x)· f´(x)

y = tgx

y´= 1+ tg2x=

sec2x = [pic 13]

y = tg f(x)

y´= (1+tg2x)· f´(x)

y = arc senx

y´=[pic 14]

y = arc senf(x)

     y´= [pic 15]

y = arc cosx        

y´= [pic 16]         

y = arc cosf(x)          

y´= [pic 17]

y = arc tgx

y´=[pic 18]

y = arc tgf(x)

y´=[pic 19]