Sustituimos .
Luego se aplica una cadena de reglas. Multiplicamos por :
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Como resultado de la secuencia de reglas:
Simplificamos:
Respuesta:
/ / tan(x)\\ | \2 /| / tan(x)\ / tan(x) \ \x / \2 / |2 tan(x) / 2 \ | 3 *x *|------- + 2 *\1 + tan (x)/*log(2)*log(x)|*log(3) \ x /
/ / tan(x)\\ | \2 /| / tan(x)\ / 2 2 / 2 \ / tan(x)\ 2 \ tan(x) \x / \2 / | 1 tan(x) /1 / 2 \ \ / 2 \ 2 2*\1 + tan (x)/*log(2) tan(x) \2 / /1 / 2 \ \ / 2 \ | 2 *3 *x *|- -- + 2 *|- + \1 + tan (x)/*log(2)*log(x)| + \1 + tan (x)/ *log (2)*log(x) + ---------------------- + 2 *x *|- + \1 + tan (x)/*log(2)*log(x)| *log(3) + 2*\1 + tan (x)/*log(2)*log(x)*tan(x)|*log(3) | 2 \x / x \x / | \ x /
/ / tan(x)\\ / 2 \ | \2 /| / tan(x)\ | 3 3 / 2 \ 2 / 2 / 2 \ \ / 2 \ 2 tan(x) 3 / tan(x)\ 3 / 2 \ 2 / tan(x)\ / 2 / 2 \ \ | tan(x) \x / \2 / |2 2*tan(x) /1 / 2 \ \ / 2 \ 3 3*\1 + tan (x)/*log(2) / 2 \ tan(x) /1 / 2 \ \ | 1 / 2 \ 2 2*\1 + tan (x)/*log(2) / 2 \ | 3*\1 + tan (x)/ *log (2) 2*tan(x) 2*2 /1 / 2 \ \ 2 2*tan(x) \2 / /1 / 2 \ \ 2 / 2 \ 6*\1 + tan (x)/*log(2)*tan(x) / 2 \ 2 tan(x) \2 / /1 / 2 \ \ | 1 / 2 \ 2 2*\1 + tan (x)/*log(2) / 2 \ | | 2 *3 *x *|-- + 2 *|- + \1 + tan (x)/*log(2)*log(x)| + \1 + tan (x)/ *log (2)*log(x) - ---------------------- + 2*\1 + tan (x)/ *log(2)*log(x) + 3*2 *|- + \1 + tan (x)/*log(2)*log(x)|*|- -- + \1 + tan (x)/ *log (2)*log(x) + ---------------------- + 2*\1 + tan (x)/*log(2)*log(x)*tan(x)| + ------------------------ + 2 *x *|- + \1 + tan (x)/*log(2)*log(x)| *log (3) + 3*2 *x *|- + \1 + tan (x)/*log(2)*log(x)| *log(3) + 4*tan (x)*\1 + tan (x)/*log(2)*log(x) + ----------------------------- + 6*\1 + tan (x)/ *log (2)*log(x)*tan(x) + 3*2 *x *|- + \1 + tan (x)/*log(2)*log(x)|*|- -- + \1 + tan (x)/ *log (2)*log(x) + ---------------------- + 2*\1 + tan (x)/*log(2)*log(x)*tan(x)|*log(3)|*log(3) | 3 \x / 2 \x / | 2 x | x \x / \x / x \x / | 2 x | | \x x \ x / \ x / /