Se aplica la regla de la derivada de una multiplicación:
; calculamos :
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
; calculamos :
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Como resultado de:
Simplificamos:
Respuesta:
/ x\ / x \ / x\ \x / x - 1 |x x | \x / x - 1 /x - 1 \ x *x *|-- + x *(1 + log(x))*log(x)| + x *x *|----- + log(x)| \x / \ x /
/ -1 + x \ / x\ | 2 2 - ------ / 2 \ | \x / -1 + x |/-1 + x \ x x | 1 log(x) x /1 \ 2 2*(1 + log(x))| x /1 \ /-1 + x \| x *x *||------ + log(x)| + ---------- + x *|- -- + ------ + x *|- + (1 + log(x))*log(x)| + (1 + log(x)) *log(x) + --------------| + 2*x *|- + (1 + log(x))*log(x)|*|------ + log(x)|| |\ x / x | 2 x \x / x | \x / \ x /| \ \ x / /
/ 2*(-1 + x) / -1 + x\ /-1 + x \ / -1 + x\ \ / x\ | 3 / 3 2 \ 3 - ---------- 3*|2 - ------|*|------ + log(x)| | 2 2 - ------| / 2 \| \x / -1 + x |/-1 + x \ x |2 3 2*x /1 \ 3 log(x) 3*(1 + log(x)) 3*(1 + log(x)) 3*(1 + log(x))*log(x) x /1 \ / 1 log(x) 2 2*(1 + log(x))\| x \ x / \ x / x /1 \ |/-1 + x \ x | x /-1 + x \ | 1 log(x) x /1 \ 2 2*(1 + log(x))|| x *x *||------ + log(x)| + x *|-- + -- + x *|- + (1 + log(x))*log(x)| + (1 + log(x)) *log(x) - ------ - -------------- + --------------- + --------------------- + 3*x *|- + (1 + log(x))*log(x)|*|- -- + ------ + (1 + log(x)) *log(x) + --------------|| - -------------- + -------------------------------- + 3*x *|- + (1 + log(x))*log(x)|*||------ + log(x)| + ----------| + 3*x *|------ + log(x)|*|- -- + ------ + x *|- + (1 + log(x))*log(x)| + (1 + log(x)) *log(x) + --------------|| |\ x / | 3 2 \x / 2 2 x x \x / | 2 x x || 2 x \x / \\ x / x / \ x / | 2 x \x / x || \ \x x x x \ x // x \ x //