a Derivadas de funciones trascendentes f(x)=sin(3x-1) d
dx sinu = cosu du
dx f'(x)= cos(3x-1)(3) f'(x)=3cos(3x-1) _________________________________________________________________ f(x)= tan(3x)d
dx tanu = sec2(u)du
dx f'(x)=sec2(3x)(1
3 x2/3)f'(x)=sec2(3x)
3 x2/3_________________________________________________________________ f(x)=sec(1-x-x3)d
dx secu= secu tanu du
dx f'(x)=sec(1-x-x3) tan(1-x-x3)(-1-3x2) f'(x)=(-1-3x2)sec(1-x-x3) tan(1-x-x3)_________________________________________________________________ f(x)=(sin2x)(cos3x)(tan4x)uvd
dxuv=ud
dxv+vd
dxud
dx tanu = sec2(u)du
dx d
dx cos u=-sen u du
dx d
dx sinu = cosu du
dxf'(x)=(sin2x)(cos3x)(sec24x(4))+(tan4x)( (sin2x)(-sin3x(3)) +( (cos2x (2))( cos3x) )f'(x)=4(sin2x)(cos3x)(sec24x)+(tan4x)( -3(sin2x)(sin3x) +( 2(cos2x )( cos3x) )_________________________________________________________________ f(x) = arcsin(5x-2) d
dxarcsinu=1
1-u2du
dx f'(x)=1
1-(5x-2)2(5) f'(x)=5
1-(5x-2)2 _________________________________________________________________ f(x)=arcsec(1
x2) 1
x2=x-2 d
dxarcsecu=1
uu2-1du
dx f'(x)=1
1
x2(1
x2)2-1(-2
x3) f'(x)=(1)(-2)
(1
x2)((1
x2)2-1)(x3)=-2
(x-2)(x3)((1
x2)2-1)f'(x)=(1)(-2)
x((1
x2)2-1)=-2
x((1
x2)(1
x2)-1)=-2
x((1
x4)-1) _________________________________________________________________ f(x)=arccot(tanx3) sec2u-tan2u=1sec2u=1+tan2u d
dxarccotu=-1
1+u2du
dxd
dx tanu = sec2(u)du
dx f'(x)=-1
1+(tanx3)2sec2(x3)3x2f'(x)=-3x2sec2(x3)
1+(tanx3)2=-3x2sec2(x3)
1+tan2(x3)=-3x2sec2(x3)
sec2(x3)=-3x2 _________________________________________________________________ f(x)=log(x4-4x2)d
dxlogu=loge
udu
dxf'(x)=loge
x4-4x2(4x3-8x)f'(x)=loge (4x3-8x)
x4-4x2 f(x)=sin5x2
log2x2 d
dx(u
v)=vd
dxu-ud
dxv
v2 f'(x)=(log2x2)(cos5x2 (10x)) - ( (sin5x2) (loge
2x24x))
log22x2 _________________________________________________________________ f(x)=2x-2 d
dxau=aulna du
dx f'(x)=2x-2ln2 (1)=2x-2ln2 _________________________________________________________________ f(x)=(3x)2x d
dxuv=vuv-1du
dx+uv lnudu
dx No lo ocupo d
dxlnu = 1
udu
dx=u'
u ln32=2ln3 y=(3x)2x lny = ln(3x)2x lny = 2x ln(3x) y'
y = (2) ln(3x) +(2x)(3
3x) y'
y = 2ln(3x) +(2x)(1
x)y'
y = 2ln(3x) +(2x
x)y'
y = 2ln(3x) +2y'
y = 2ln(3x) +2 y'=(y) (2ln(3x) +2) y'=(3x)2x (2ln(3x) +2) _________________________________________________________________ f(x)=(x2+x+1)sinx y=(x2+x+1)sinx ln y=ln (x2+x+1)sinx ln y=sinx ln (x2+x+1) y'
y=(sinx) (ln (x2+x+1))y'
y=((cos x) (ln (x2+x+1)))+((sinx)(2x+1
x2+x+1)) y'=(x2+x+1)sinx((cos x) (ln (x2+x+1))+(sinx)(2x+1
x2+x+1)) 
