find-all-second-order-partial-derivatives-f-x-y-xe-x-y-y-x-

Question Number 57997 by peter frank last updated on 15/Apr/19

f i n d a l l s e c o n d o r d e r p a r t i a l

d e r i v a t i v e s

f (x, y) = {x e}^{x^{y}} . y^{x}

Commented by MJS last updated on 16/Apr/19

for x :

f = u v w

f^{'} = u^{'} v w + {u v}^{'} w + {u v w}^{'}

f^{″} = u^{″} v w + {u v}^{″} w + {u v w}^{″} + 2 (u^{'} v^{'} w + u^{'} {v w}^{'} + {u v}^{'} w^{'})

u = x u^{'} = 1 u^{″} = 0

v = y^{x} v^{'} = y^{x} \ln y v^{″} = y^{x} {(\ln y)}^{2}

w = e^{x^{y}} w^{'} = x^{y - 1} y e^{x^{y}} w^{″} = x^{y - 2} y ((x^{y} + 1) y - 1) e^{x^{y}}

Commented by MJS last updated on 16/Apr/19

is it an imposition for bad behavior? ��