# 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.

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

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

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

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

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

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).