Question

Calcule em cada caso abaixo as derivadas parciais;

a) f(x,y) = y² ln(x² + y²)



b) f(x,y) = xsen(yz) + ysen(xz)

Answer 1

a)

$f(x,y) = y^2*ln(x^2+y^2)\\\\ f_x = \frac{y^2*2x}{x^2+y^2}\\\\ \large\boxed{f_x=\frac{2xy^2}{x^2+y^2}}$

$f_y=2y*ln(x^2+y^2)+\frac{y^2*2y}{x^2+y^2}\\\\ \large\boxed{f_y=2y*ln(x^2+y^2)+\frac{2y^3}{x^2+y^2}}$

b)

$f(x,y,z) = xsen(yz)+ysen(xz)\\\\ \large\boxed{f_x=sen(yz)+yzcos(xz)}$

$f(x,y,z) = xsen(yz)+ysen(xz)\\\\ \large\boxed{f_y=xzcos(yz)+sen(xz)}$

$f(x,y,z) = xsen(yz)+ysen(xz)\\\\ \large\boxed{f_z=xycos(yz)+yxcos(xz}}$