Formulario para C ´alculo Diferencial
i. dc
dx =0
ii. dx
dx =1
iii. d(u+v)
dx =du
dx +dv
dx
iv. d(c·v)
dx =cdv
dx
v. d(u·v)
dx =udv
dx +vdu
dx
vi. d(vn)
dx =nvn−1dv
dx
vii. d
dx u
v=
vdu
dx −udv
dx
v2
viii. d(sin v)
dx =cos vdv
dx
ix. d(cos v)
dx =−sin vdv
dx
x. d(tan v)
dx =sec2vdv
dx
xi. d(cot v)
dx =−csc2vdv
dx
xii. d(sec v)
dx =sec vtan vdv
dx
xiii. d(csc v)
dx =−csc vcot vdv
dx
xiv. d(arcsin v)
dx =1
√1−v2
dv
dx
xv. d(arccos v)
dx =−1
√1−v2
dv
dx
xvi. d(arctan v)
dx =1
1+v2
dv
dx
xvii. d(arccot v)
dx =−1
1+v2
dv
dx
xviii. d(arcsec v)
dx =1
v√v2−1
dv
dx
xix. d(arccsc v)
dx =−1
v√v2−1
dv
dx
xx. d(ln v)
dx =1
v
dv
dx
xxi. d(logav)
dx =logae
v
dv
dx
xxii. d(av)
dx =avln adv
dx
xxiii. d(ev)
dx =evdv
dx
xxiv. d(uv)
dx =v·uv−1+ln u·uvdv
dx
xxv. dy
dx =dy
dv ·dv
dx
xxvi. dy
dx =1
dx
dy
Formulario para C ´alculo Integral
i. Z(dv +dw) = Zdv +Zdw
ii. Za dv =aZdv
iii. Zdx =x+C
iv. Zvndv =vn+1
n+1+C
v. Zdv
v=ln |v|+C
vi. Zavdv =av
ln a+C
vii. Zevdv =ev+C
viii. Zln v dv =vln v−v+C
ix. Zsin v dv =−cos v+C
x. Zcos v dv =sin v+C
xi. Zsec2v dv =tan v+C
xii. Zcsc2v dv =−cot v+C
xiii. Zsec vtan v dv =sec v+C
xiv. Zsec v dv =ln (sec v+tan v)+
C
xv. Zdv
a2−v2=1
2aln a+v
a−v+
C
xvi. Zdv
a2+v2=1
aarctan v
a+C
xvii. Zdv
v2−a2=1
2aln v−a
v+a+
C
xviii. Zdv
√a2−v2=arcsin v
a+C
xix. Zdv
√v2±a2=ln v+√v2±a2+
C
xx. Z√a2−v2dv =v
2√a2−v2+
a2
2arcsin v
a+C
xxi. Z√v2±a2dv =v
2√v2±a2±
a2
2ln v+√v2±a2+C
xxii. Zu dv =u·v−Zv du
Sustituciones
Trigonom´etricas
3√a2−u2→h´
agase
u=asin z→acos z
3√a2+u2→h´
agase
u=atan z→asec z
3√u2−a2→h´
agase
u=asec z→atan z
www.aprendematematicas.org.mx
