# How to calculate f(x,y,z)=x^3sqrty+4z^3y^2-xyz+x^2 - 3sqrt(z^5) by first order of partial derivative?

Jul 28, 2018

$f \left(\boldsymbol{x}\right) = {x}^{3} \sqrt{y} + 4 {z}^{3} {y}^{2} - x y z + {x}^{2} - 3 \sqrt{{z}^{5}}$

Using the power rule:

• $\left\{\begin{matrix}{f}_{x} = 3 {x}^{2} \sqrt{y} - y z + 2 x \\ {f}_{y} = \frac{1}{2} {x}^{3} / \sqrt{y} + 8 {z}^{3} y - x z \\ {f}_{z} = 12 {z}^{2} {y}^{2} - x y - \frac{15}{4} \sqrt{{z}^{3}}\end{matrix}\right.$

These are the partial derivatives. It is assumed that is what you meant.