Answer to Question #135772 in Calculus for Promise Omiponle

Question

Find the first partial derivatives of f(x,y,z)=z arctan(y/x) at the point (4, 4, -4).

A. ∂f/∂x(4,4,−4)=
B. ∂f/∂y(4,4,−4)=
C. ∂f/∂z(4,4,−4)=

Answer 1

A. ∂f/∂x(4,4,−4)= (-4*-4)/(4²⁺4²)

=16/32

=1/2

B. ∂f/∂y(4,4,−4)=(-4*4)/(4²⁺4²)

=-16/32

=-1/2

C. ∂f/∂z(4,4,−4)=arctan(4/4)

=arctan 1

=$\pi$ /4