Formulario Esencial de Derivadas e Integrales: Cálculo Fundamental

y = c

y′ = 0

c·x

y = c·x

y′ = c

c·x²/2

y = xⁿ

y′ = n·x^n-1

xⁿ⁺¹/(n+1)

y = x^-n

y′ = -1/(n·x^n-1)

x^-n+1/(-n+1)

y = x^½

y′ = 1/(2·x^½)

2·x^3/2/3

y = x^a/b

y′ = (a/b)·x^(a/b)-1

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′ = sen x/cos²x

ln |tg(x/2)|

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]

y = arccosec x

y′ = -1/[x·(x² − 1)^½]

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 = sech x

y′ = -sech x·tgh x

y = cosech x

y′ = -cosech x·cotgh x

y = ln x

y′ = 1/x

x·(ln x - 1)

y = log_ax

y′ = 1/(x·ln(a))

x·(log_ax - 1/ln(a))

y = e^x

y′ = e^x

e^x

y = a^x

y′ = a^x·ln(a)

a^x/ln(a)

y = x^x

y′ = x^x·(ln x + 1)

y = e^u

y′ = e^u·u′

y = u·v

y′ = u′·v + v′·u

∫u·dv + ∫v·du

y = u/v

y′ = (u′·v - v′·u)/v²

y = u^v

y′ = u^v·(v′·ln(u) + v·u′/u)

y = log_uv

y′ = (v′·u·ln(u) - u′·v·ln(v))/(v·u·(ln(u))²)