ecuacions diferencials

d_{x}[ pluf[n]-arc-sin(x) ] = ...

... ( pluf[n]-arc-sin(x) )^{n}·( 1+(-1)·( pluf[n]-arc-sin(x) )^{2} )^{(1/2)}

d_{x}[ pluf[n]-arc-cos(x) ] = ...

... (-1)·( pluf[n]-arc-cos(x) )^{n}·( 1+(-1)·( pluf[n]-arc-cos(x) )^{2} )^{(1/2)}

d_{x}[y(x)] = ( sin(y(x)) )^{n}

y(x) = arc-sin( pluf[n]-arc-sin(x) )

d_{x}[y(x)] = ( cos(y(x)) )^{n}

y(x) = arc-cos( pluf[n]-arc-cos(x) )

d_{x}[ pluf[n]-arc-tan(x) ] = ...

... ( pluf[n]-arc-tan(x) )^{n}·( 1+( pluf[n]-arc-tan(x) )^{2} )

d_{x}[ pluf[n]-arc-cot(x) ] = ...

... (-1)·( pluf[n]-arc-cot(x) )^{n}·( 1+( pluf[n]-arc-cot(x) )^{2} )

d_{x}[y(x)] = ( tan(y(x)) )^{n}

y(x) = arc-tan( pluf[n]-arc-tan(x) )

d_{x}[y(x)] = ( cot(y(x)) )^{n}

y(x) = arc-cot( pluf[n]-arc-cot(x) )

arc-cos(x)+arc-sin(-x) = (3/2)·pi

d_{x}[ arc-sin(-x) ] = ( 1/(1+(-1)·(-x)^{2})^{(1/2)} )

d_{x}[ arc-cos(x) ] = (-1)·( 1/(1+(-1)·x^{2})^{(1/2)} )

pi+(pi/2) = 0+(3/2)·pi = 2pi+(-1)·(pi/2) = ...

... (pi/4)+(5/4)·pi = (3/4)·pi+(3/4)·pi = (7/4)·pi+(-1)·(pi/4) = ...

... (1/3)·pi+(7/6)·pi = (1/6)·pi+(4/3)·pi

arc-cot(x)+arc-tan(x) = k

d_{x}[ arc-tan(x) ] = ( 1/(1+x^{2}) )

d_{x}[ arc-cot(x) ] = (-1)·( 1/(1+x^{2}) )

arc-coth(x)+(-1)·arc-tanh(x) = k

d_{x}[ arc-tanh(x) ] = ( 1/(1+(-1)·x^{2}) ) = d_{x}[ arc-coth(x) ]

int[ arc-tanh(x) ] d[x] = x·arc-tanh(x)+(1/2)·( ln(1+(-1)·x^{2}) )

int[ arc-coth(x) ] d[x] = x·arc-coth(x)+(1/2)·( ln(1+(-1)·x^{2}) )