y = k y' = 0 y = x y' = 1 y = k x y' = k y = k u y' = k u' y = u +- v y' = u' +- v' y = u v y' = u' v + u v' y = u/v y' = (u' v - u v') / v^2 y = raiz( x ) y' = 1 / ( 2 raiz( x ) ) y = raiz( u ) y' = u'/ ( 2 raiz( u ) ) y = raiz( n , x ) y' = 1 / ( n raiz( n , x^(n-1) ) ) y = raiz( n , u ) y' = u'/ ( n raiz( n , u^(n-1) ) ) y = x^m y' = m x^(m-1) y = u^m y' = m u^(m-1) u' y = e^x y' = e^x y = e^u y' = e^u u' y = k^x y' = k^x ln(k) y = k^u y' = k^u ln(k) u' y = ln(x) y' = 1/x y = ln(u) y' = u'/u y = log_a(x) y' = log_a(e) 1/x y = log_a(u) y' = log_a(e) u'/u y = sen(x) y' = cos(x) y = cos(x) y' = -sen(x) y = sen(u) y' = cos(u) u' y = cos(u) y' = -sen(u) u' y = tag(x) y' = 1/cos^2(x) y = tag(u) y' = u'/cos^2(u) y = cotag(x) y' = -1/sen^2(x) y = cotag(u) y' = -u'/sen^2(u) y = arc sen(x) y' = 1/raiz(1-x^2) y = arc sen(u) y' = u'/raiz(1-u^2) y = arc cos(x) y' = -1/raiz(1-x^2) y = arc cos(u) y' = -u'/raiz(1-u^2) y = arc tag(x) y' = 1/(1+x^2) y = arc tag(u) y' = u'/(1+u^2) y = arc cotag(x) y' = -1/(1+x^2) y = arc cotag(u) y' = -u'/(1+u^2) Regla de la cadena: y = f(u) y' = dy / du u = g(x) u' = du / dx dy / dx = y' u'