defensa nacional



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
(xⁿ)’=nxⁿ⁻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

(arctgx)’=1/(1+x²) (aˣ)’=aˣlna

(eˣ)’=eˣ (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

sen²α +cos²α=1
tg α= sen α/cos α cotg α= cos α/sen α
sec α= 1/cos α cosec α=1/sen α

sen(-α)=-sen α cos(-α)=cos α tg(-α)=-tg αsen(π/2-α)=cosα cos(π/2-α)=senα
tg(π/2-α)=cotgα

sen(π/2+α)=cosα cos(π/2+α)=-senα
tg(π/2+α)=-cotgα

sen(π-α)=senα cos(π-α)=-cosα tg(π-α)=-tgα

sen(π+α)=-senα cos(π+α)=-cosαtg(π+α)=tgα

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.senbtg(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.cosacos2a=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
(xⁿ)’=nxⁿ⁻¹ (√x)’=1/2√x

(sen x)’=cos x (cos x)’=-sen x

(tgx)’=1/cos²x (cotg x)’=-1/sen²x

(arcsen x)’=1/√1-x² (arccos x)’=-1/√1-x²

(arctg x)’=1/(1+x²) (aˣ)’=aˣlna

(eˣ)’=eˣ (ln x)’=1/x


Regla de la...