# Thread: Is this formula correct?

1. ## Is this formula correct?

hi everyone

need help to verify this formula for partial derivative, is this correct?thank you in advance for all help & support.

$\frac{\partial z}{\partial x}= - \frac {F_x}{F_z}$
$\frac{\partial z}{\partial y}= - \frac {F_y}{F_z}$

Find $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$ for

a) xyz - cos(x + y + z)=0
$F_x = yz + sin(x + y + z)$,
$F_z=xy+sin(x+y+z)$
$F_y=xz+sin(x+y+z)$

$\frac{\partial z}{\partial x}= - \frac {F_x}{F_z}$
$=-\frac{yz + sin(x + y + z)}{xy+sin(x+y+z)}$
$\frac{\partial z}{\partial y}= - \frac {F_y}{F_z}$
$-\frac{xz+sin(x+y+z)}{xz+sin(x+y+z)}$

b) $4ln(4xyz) + sin(xz^2))=0$
$F_x=\frac{4}{x}+z^2cos(xz^2)$
$F_y=\frac{4}{y}$
$F_z=\frac{4}{x}+2xz^2cos(xz^2)$
$\frac{\partial z}{\partial x}=-\frac{\frac{4}{x}+z^2cos(xz^2)}{\frac{4}{x}+2xz^2c os(xz^2)}$
$\frac{\partial z}{\partial y}=\frac{\frac{4}{y}}{\frac{4}{x}+2xz^2cos(xz^2)}$

really appreciate if someone can help verify & confirm,thank you in advance for all your kind help & support,really appreciate.

Thank you & regards

2. All good up until Fz in b).