Question

Encontre as derivadas de ordem superior (fyx e fxy) pedidas a seguir: f(x,y) = xy² - 5y + 6

Answer 1

Explicação passo-a-passo:

Derivadas parciais

Dada a função :

$\sf{ \red{ f(x,y)~=~ xy^2 - 5y + 6 } }$

Item A) Calcular a fyx :

$\sf{ \dfrac{\partial f}{\partial y}~=~ f_{y}~=~ 2xy - 5 + 0 }$

$\iff \sf{ f_{y}~=~ 2xy - 5 }$

$\sf{ \dfrac{\partial }{\partial x}\Big( \dfrac{ \partial f}{\partial y}\Big) ~=~ f_{yx}~=~ 2y }$

$\pink{ \iff \boxed{ \boxed{ \sf{ f_{yx}~=~ 2y } } } \sf{ \longleftarrow Resposta } }$

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Item B) Achar a fxy :

$\sf{ \dfrac{\partial f}{\partial x}~=~ f_{x}~=~ y^2 - 0 + 0 }$

$\iff \sf{ f_{x}~=~ y^2 }$

$\sf{ \dfrac{\partial }{\partial y}\Big( \dfrac{\partial f}{\partial x}\Big)~=~ f_{xy}~=~2y }$

$\green{ \iff \boxed{\boxed{\sf{ f_{xy}~=~2y } } } \sf{ \longleftarrow Resposta } }$

Espero ter ajudado bastante!)