Partial Derivatives of $F(x,y,z) = \log(z + \sin(y^2 -x))$

Question

Partial derivatives with respect to $x$, $y$ and $z$.

Thank you!

Answer 1

If you calculate $\dfrac{\partial F}{\partial x}$, that means you hold $y$ and $z$ fixed. So: $\dfrac{\partial F}{\partial x} = \dfrac{-cos(y^2 - x)}{z + sin(y^2 - x)}$

$\dfrac{\partial F}{\partial y} = \dfrac{2y \cdot cos(y^2 - x)}{z + sin(y^2 - x)}$

$\dfrac{\partial F}{\partial z} = \dfrac{1}{z + sin(y^2 - x)}$