log(x) / 3 \ \cos (x)*x/
(cos(x)^3*x)^log(x)
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
log(x) / / 3 \ / 3 2 \ \ / 3 \ |log\cos (x)*x/ \cos (x) - 3*x*cos (x)*sin(x)/*log(x)| \cos (x)*x/ *|-------------- + -------------------------------------| | x 3 | \ x*cos (x) /
/ 2 \ |/ / 3 \ (-cos(x) + 3*x*sin(x))*log(x)\ | log(x) ||- log\x*cos (x)/ + -----------------------------| / 3 \ / 2 2 \ | / 3 \ |\ cos(x) / log\x*cos (x)/ 3*\x*cos (x) - 2*x*sin (x) + 2*cos(x)*sin(x)/*log(x) 2*(-cos(x) + 3*x*sin(x)) (-cos(x) + 3*x*sin(x))*log(x) 3*(-cos(x) + 3*x*sin(x))*log(x)*sin(x)| \x*cos (x)/ *|--------------------------------------------------- - -------------- - ---------------------------------------------------- - ------------------------ + ----------------------------- - --------------------------------------| | x x 2 x*cos(x) x*cos(x) 2 | \ cos (x) cos (x) / --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- x
/ / / 3 \ / 2 2 \ \ \ | 3 / / 3 \ (-cos(x) + 3*x*sin(x))*log(x)\ |log\x*cos (x)/ 2*(-cos(x) + 3*x*sin(x)) 3*\x*cos (x) - 2*x*sin (x) + 2*cos(x)*sin(x)/*log(x) (-cos(x) + 3*x*sin(x))*log(x) 3*(-cos(x) + 3*x*sin(x))*log(x)*sin(x)| | | / / 3 \ (-cos(x) + 3*x*sin(x))*log(x)\ 3*|- log\x*cos (x)/ + -----------------------------|*|-------------- + ------------------------ + ---------------------------------------------------- - ----------------------------- + --------------------------------------| | log(x) | |- log\x*cos (x)/ + -----------------------------| / 3 \ / 2 2 \ / 3 2 3 2 \ \ cos(x) / | x x*cos(x) 2 x*cos(x) 2 | / 2 2 \ 2 / 2 2 \ | / 3 \ | \ cos(x) / 2*log\x*cos (x)/ 9*\x*cos (x) - 2*x*sin (x) + 2*cos(x)*sin(x)/ 3*(-cos(x) + 3*x*sin(x))*log(x) 3*\3*cos (x) - 6*sin (x)*cos(x) + 2*x*sin (x) - 7*x*cos (x)*sin(x)/*log(x) \ cos (x) cos (x) / 6*(-cos(x) + 3*x*sin(x)) 18*\x*cos (x) - 2*x*sin (x) + 2*cos(x)*sin(x)/*log(x)*sin(x) 12*sin (x)*(-cos(x) + 3*x*sin(x))*log(x) 9*(-cos(x) + 3*x*sin(x))*sin(x) 2*(-cos(x) + 3*x*sin(x))*log(x) 6*\x*cos (x) - 2*x*sin (x) + 2*cos(x)*sin(x)/*log(x) 6*(-cos(x) + 3*x*sin(x))*log(x)*sin(x)| \x*cos (x)/ *|- --------------------------------------------------- + ---------------- - --------------------------------------------- - ------------------------------- - -------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------ - ------------------------------------------------------------ - ---------------------------------------- - ------------------------------- - ------------------------------- + ---------------------------------------------------- + --------------------------------------| | 2 2 2 cos(x) 3 x 2 3 3 2 2 2 2 | \ x x x*cos (x) cos (x) x *cos(x) cos (x) cos (x) x*cos (x) x *cos(x) x*cos (x) x*cos (x) / ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- x