Question

Calcule as derivadas parciais de 1ª ordem da função
f(x, y) = 3x² - 7xy + 5y³ – (3x + y) – 1
em um ponto (x0, y0) de sua escolha

Answer 1

$\mathtt{f(x, y)=3{x}^{2}-7xy+5{y}^{3}-(3x+y)-1}$

$\mathtt{\dfrac{\partial~f}{\partial~x}=6x-7y+0-3}$

$\mathtt{\dfrac{\partial~f}{\partial~x}=6x-7y-3}$

$\mathtt{\dfrac{\partial~f}{\partial~y}= - 7x + 15 {y}^{2} - 1 }$

Answer 2

$\dfrac{\partial f}{\partial x} =3\cdot2x-7\cdot1y+0-3\cdot1+0-0=6x-7y-3$

$\dfrac{\partial f}{\partial y}=0-7x\cdot1+5\cdot3y^2-0+1-0=-7+15y^2$

Aplicando no ponto P(0,0):

$f_x(0,0)=6(0)-7(0)-3=-3\\\\f_y(0,0)=-7(0)+15(0)^2=0$