DERIVADAS

(c)'=0 (x)'=1 (u±v)'=u'±v' (cu)'=cu'

(uv)'=u'v+uv' (u/v)'=(u'v-uv')/v²

(c/v)'=-cv'/v²

(x )'=nx ¹ ("x)'=1/2"x

(sen x)'=cos x (cos x)'=-sen x

(tg x)'=1/cos²x (cotg x)'=-1/sen²x

(arcsen x)'=1/"1-x² (arccos x)'=-1/"1-x²

(arctg x)'=1/(1+x²) (a)'=alna

(e)'=e (ln x)'=1/x

Regla de la cadena:

(f(g(h(x))))'=f'(g(h(x))).g'(h(x)).h'(x)

LOGARITMOS

Log(a.b)=log a +log b Log(a/b)=log a -log b

Log(bª)=a.log b

TRIGONOMETRÍA

sen² +cos²=1

tg = sen /cos  cotg = cos /sen 

sec = 1/cos  cosec =1/sen 

sen(-)=-sen  cos(-)=cos  tg(-)=-tg 

sen(/2-)=cos cos(/2-)=sen

tg(/2-)=cotg

sen(/2+)=cos cos(/2+)=-sen

tg(/2+)=-cotg

sen(-)=sen cos(-)=-cos tg(-)=-tg

sen(+)=-sen cos(+)=-cos tg(+)=tg

sen(a+b)=sena.cosb+senb.cosa

cos(a+b)=cosa.cosb-sena.senb

tg(a+b)=(tga+tgb)/(1-tga.tgb)

sen(a-b)=sena.cosb-senb.cosa

cos(a-b)=cosa.cosb+sena.senb

tg(a-b)=(tga-tgb)/(1+tga.tgb)

sena+senb=2sen((a+b)/2).cos((a-b)/2)

cosa+cosb=2cos((a+b)/2).cos((a-b)/2)

sena-senb=2sen((a-b)/2).cos((a+b)/2)

cosa-cosb=-2sen((a+b)/2).sen((a-b)/2)

sen2a=2sena.cosa cos2a=cos²a-sen²a

tg2a=2tga/(1-tg²a)

sen(a/2)= ±"(1-cosa)/2 cos(a/2)= ±"(1+cosa)/2

tg(a/2)= ± "(1-cosa)/(1+cosa)

DERIVADAS

(c)'=0 (x)'=1 (u±v)'=u'±v' (cu)'=cu'

(uv)'=u'v+uv' (u/v)'=(u'v-uv')/v²

(c/v)'=-cv'/v²

(x )'=nx ¹ ("x)'=1/2"x

(sen x)'=cos x (cos x)'=-sen x

(tg x)'=1/cos²x (cotg x)'=-1/sen²x

(arcsen x)'=1/"1-x² (arccos x)'=-1/"1-x²

(arctg x)'=1/(1+x²) (a)'=alna

(e)'=e (ln x)'=1/x

Regla de la cadena:

(f(g(h(x))))'=f'(g(h(x))).g'(h(x)).h'(x)

LOGARITMOS

Log(a.b)=log a +log b Log(a/b)=log a -log b

Log(bª)=a.log b

TRIGONOMETRÍA

sen² +cos²=1

tg = sen /cos  cotg = cos /sen 

sec = 1/cos  cosec =1/sen 

sen(-)=-sen  cos(-)=cos  tg(-)=-tg 

sen(/2-)=cos cos(/2-)=sen

tg(/2-)=cotg

sen(/2+)=cos cos(/2+)=-sen

tg(/2+)=-cotg

sen(-)=sen cos(-)=-cos tg(-)=-tg

sen(+)=-sen cos(+)=-cos tg(+)=tg

sen(a+b)=sena.cosb+senb.cosa

cos(a+b)=cosa.cosb-sena.senb

tg(a+b)=(tga+tgb)/(1-tga.tgb)

sen(a-b)=sena.cosb-senb.cosa

cos(a-b)=cosa.cosb+sena.senb

tg(a-b)=(tga-tgb)/(1+tga.tgb)

sena+senb=2sen((a+b)/2).cos((a-b)/2)

cosa+cosb=2cos((a+b)/2).cos((a-b)/2)

sena-senb=2sen((a-b)/2).cos((a+b)/2)

cosa-cosb=-2sen((a+b)/2).sen((a-b)/2)

sen2a=2sena.cosa cos2a=cos²a-sen²a

tg2a=2tga/(1-tg²a)

sen(a/2)= ±"(1-cosa)/2 cos(a/2)= ±"(1+cosa)/2

tg(a/2)= ± "(1-cosa)/(1+cosa)