Question

3. Calcule as derivadas parciais de f(x, y ) = 9 - x2 - 7y3, fx (3, 1) e fy​​​​​​​ (3, 1).


A. fx = -21, fy = - 6


B. fx = 21, fy = - 6


C. fx = - 6, fy = - 21


D. fx = 6, fy = 21


E. fx = 3, fy = - 13

Answer 1

Conteúdo:

• Derivadas Parciais

✍ Dada função:

$\huge { \sf F(x,y) = 9 - x^2 -7y^3 }$

✎ Iremos fazer assim:

$\huge {\boxed {\blue {\sf \cfrac{ \partial f }{\partial x} \: (x,y) = f_x(x,y) = -2x }}}$

$\huge {\boxed {\blue {\sf \cfrac{ \partial f }{\partial y} \: (x,y) = f_y(x,y) = -21y^2 }}}$

➡️ Agora temos de substituir:

$\huge {\boxed {\purple {\sf \cfrac{ \partial f}{ \partial x} (3,1) = -2x = -2 \centerdot 3=-6 }}}$

                                               $\huge { \updownarrow }$

$\huge {\boxed {\green {\sf \cfrac{ \partial f}{ \partial y} (3,1) = -21y^2 = -21\centerdot 1^2=-21 }}}$

→    Resposta:

$\huge { \bullet \quad \quad Letra \:\: C }$

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