No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
log(x)*sin(x) //sin(x) \ (x*cos(x) + sin(x))*log(x)\ (x*sin(x)) *||------ + cos(x)*log(x)|*log(x*sin(x)) + --------------------------| \\ x / x /
/ /sin(x) \\ | 2 (x*cos(x) + sin(x))*|------ + cos(x)*log(x)|| log(x)*sin(x) |//sin(x) \ (x*cos(x) + sin(x))*log(x)\ x*cos(x) + sin(x) /sin(x) 2*cos(x)\ (-2*cos(x) + x*sin(x))*log(x) (x*cos(x) + sin(x))*log(x) \ x /| (x*sin(x)) *|||------ + cos(x)*log(x)|*log(x*sin(x)) + --------------------------| + ----------------- - |------ + log(x)*sin(x) - --------|*log(x*sin(x)) - ----------------------------- - -------------------------- + --------------------------------------------| |\\ x / x / 2 | 2 x | x 2 x*sin(x) | \ x \ x / x /
/ /sin(x) 2*cos(x)\ \ | / /sin(x) \\ /sin(x) \ /sin(x) \ 2*(x*cos(x) + sin(x))*|------ + log(x)*sin(x) - --------| /sin(x) \ | | 3 | (x*cos(x) + sin(x))*|------ + cos(x)*log(x)|| (-2*cos(x) + x*sin(x))*|------ + cos(x)*log(x)| (x*cos(x) + sin(x))*|------ + cos(x)*log(x)| | 2 x | (x*cos(x) + sin(x))*|------ + cos(x)*log(x)|*cos(x)| log(x)*sin(x) |//sin(x) \ (x*cos(x) + sin(x))*log(x)\ / 2*sin(x) 3*sin(x) 3*cos(x)\ 3*(x*cos(x) + sin(x)) //sin(x) \ (x*cos(x) + sin(x))*log(x)\ |/sin(x) 2*cos(x)\ x*cos(x) + sin(x) (-2*cos(x) + x*sin(x))*log(x) (x*cos(x) + sin(x))*log(x) \ x /| 2*(-2*cos(x) + x*sin(x)) (3*sin(x) + x*cos(x))*log(x) 2*(x*cos(x) + sin(x))*log(x) 2*(-2*cos(x) + x*sin(x))*log(x) \ x / \ x / \ x / \ x / | (x*sin(x)) *|||------ + cos(x)*log(x)|*log(x*sin(x)) + --------------------------| - |cos(x)*log(x) - -------- + -------- + --------|*log(x*sin(x)) - --------------------- - 3*||------ + cos(x)*log(x)|*log(x*sin(x)) + --------------------------|*||------ + log(x)*sin(x) - --------|*log(x*sin(x)) - ----------------- + ----------------------------- + -------------------------- - --------------------------------------------| - ------------------------ - ---------------------------- + ---------------------------- + ------------------------------- - ----------------------------------------------- - -------------------------------------------- - --------------------------------------------------------- - ---------------------------------------------------| |\\ x / x / | 3 x 2 | 3 \\ x / x / || 2 x | 2 x 2 x*sin(x) | 2 x 3 2 x*sin(x) 2 x*sin(x) 2 | \ \ x x / x \\ x / x x / x x x x *sin(x) x*sin (x) /