ecuació geométrica y derivació de inversa

(-1)·( cosh[1:n+1](x) )^{n+1}+sinh[1:n+1](x) = (-1)

d_{x}[y] = ( y^{(n+1)}+(-1) )/( y+(-m) )

(y+(-m))·d_{x}[y] = y^{(n+1)}+(-1)

( cosh[1:n+1]( f(x) )+(-m) )·d_{x}[f(x)] = 1

sinh[1:n+1]( f(x) )+(-m)·( f(x) ) ) = x

sinh[1:n+1]-sum[(-m)]( f(x) ) = x

f(x) = anti-sinh[1:n+1]-sum[(-m)](x)

y(x) = cosh[1:n+1]( anti-sinh[1:n+1]-sum[(-m)](x) )

d_{x}[ anti-sinh[1:n+1]-sum[(-m)](x) ] = ...

... ( 1/( cosh[1:n+1]( anti-sinh[1:n+1]-sum[(-m)](x) )+(-m) ) )

f^{o(-1)}(x) = y

d_{x}[f^{o(-1)}(x)] = ( 1/d_{y}[f(y)] )

y = ln(x)

d_{x}[ln(x)] = ( 1/d_{y}[e^{y}] ) = (1/e^{y}) = (1/x)

y = arc-sin(x)

d_{x}[arc-sin(x)] = ( 1/d_{y}[sin(y)}] ) = (1/cos(y)) = ...

... ( 1/( 1+(-1)·( sin(y) )^{2} )^{(1/2)} ) = ( 1/( 1+(-1)·x^{2} )^{(1/2)} )

d_{x}[ anti-ln-pow[n](x) ] = ...

... ( y/(n·y^{n}ln(y)+y^{n}) ) = ( y/(n·ln-pow[n](y)+y^{n}) )

... ( anti-ln-pow[n](x)/(nx+( anti-ln-pow[n](x) )^{n}) )

d_{x}[ anti-e-pow[n](x) ] = ...

... ( y/(n·y^{n}e^{y}+y^{n}e^{y}y) ) = ( y/(n·e-pow[n](y)+e-pow[n](y)y) )

... ( 1/e-pow[n](y) )·( y/(n+y) ) = (1/x)·( anti-e-pow[n](x)/(n+anti-e-pow[n](x)) )

d_{x}[ anti-ln-[+]-sum[n](x) ] = ...

... ( 1/((1/y)+n) ) = ( y/(1+ny) )

... ( anti-ln-[+]-sum[n](x)/(1+n·anti-ln-[+]-sum[n](x)) )

d_{x}[ anti-e-[+]-sum[n](x) ] = ...

... ( 1/(e^{y}+n) ) = ( 1/(e^{y}+ny+n·(1+(-y)) ) = ( 1/( e-[+]-sum[n](y)+n·(1+(-y)) ) )

... ( 1/( x+n·(1+(-1)·anti-e-[+]-sum[n](x)) ) )

ln(x)+nx = c

ln-[+]-sum[n](x) = c

x = anti-ln-[+]-sum[n](c)

e^{x}+nx = c

e-[+]-sum[n](x) = c

x = anti-e-[+]-sum[n](c)

ln(x)+nx^{m+1} = c

x^{m}·( ln(x)/x^{m}+nx ) = c

x^{m}·( ln-pow[(-m)](x)+nx ) = c

x^{m}·( ln-pow[(-m)]-[+]-sum[n](x) ) = c

( ln-pow[(-m)]-pow[m]-[+]-sum[n]-pow[m](x) ) = c

( ln-[+]-sum[n]-pow[m](x) ) = c

x = anti-ln-[+]-sum[n]-pow[m](c)

e^{x}+nx^{m+1} = c

x = anti-e-[+]-sum[n]-pow[m](c)

x^{k}·ln(x)+nx^{m+1} = c

x = anti-ln-pow[k]-[+]-sum[n]-pow[m](c)

x^{k}·e^{x}+nx^{m+1} = c

x = anti-e-pow[k]-[+]-sum[n]-pow[m](c)