Ecuasiones de primer orden

1. y=ax2x-1/3+ bxx1/2-x1/3x-1/2
y'=ax53+bx-32-x-16

y'=53ax2/3-32bx-52+16x-7/66

1. fx= 2x2-1x1+x2
y'=(x1+x2d(2x2-1dx-2x2-1d(x1+x2dx(x1+x2)2y'=(x1+x2)4x-2x2+1 xd1+x212dx+(1+x2)1/2d(x)d(x)(x1+x2)2
y'= 4x21+x2-2x2+1x∙121+x212d1+x2dx+1+x2(x1+x2)2
y'=4x21+x2-2x2+1x2(1+x2)1/2∙2x+1+x2(x1+x22y'=4x21+x2-2x2+12x221+x2+1+x2x1+x22
y'= 4x21+x2-2x41+x2-2x21+x2+x21+x2+1+x2(x1+x2)2
y'=2x21+x2--2x41+x2+x21+x2+1+x2(x1+x2)2
y'=2x21+x2-2x4+x2+(1+x2)1+x2(x1+x2)2y'= 2x2+2x4-2x4+x2+1+x21+x2(x1+x2)2
y'=4x2+11+x2(x1+x2)21
y'= 4x2+1(x1+x2)21+x2

3. 1 d (1+sen x1-sen x)

1[ 1-sen x d1-senxdx-1+sen xd(1+senx)dx(1-senx)2]

1[ 1-senx*cosx-(1+senx)(-cosx)(1-senx )2]

1[*cosx-senxcosx+cosx+senxcosx(1-senx )2]

1[-2cosx(1-senx )2]y=2cosx(1-senx )2


4.- y= In (x+1+X2)
y´= 1 . d(x+1+X2)
x+1+X2 dx
y´= 1 . d(x) + d (1+ X2 )1/2x+1+X2 dx dx
y´= 1 . 1
2 (1+ X2 )1/2dx
y´= 1+ 1
2 1+x2
x(1+x2)
y´= 2 1+x2 +1
2 1+x2x 1+x2
y´= 2 1+x2 +1
2x (1+x2)
y´= 2 1+x2 +1
2x 2+x3

5.fx=℮cosxsinx
d(℮cosxsenx)
y'= ℮cosxdsenxdx+senx d℮cosxdx
y'= ℮cosx ∙cosx+senx∙℮cosxd(cosx)dx
y'=cosx ℮cosx+senx℮cosx∙-cosx
y'=cosx℮cosx-cosxsenx℮cosx