Solve z = 18 - x^2 - y^2

Simplify

z = 18 - x^{2} - y^{2}

Find the first partial derivative by treating the variable y as a constant and differentiating with respect to x

\frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (18 - x^{2} - y^{2})

Use differentiation rule \frac{\partial}{\partial x} (f (x) \pm g (x)) = \frac{\partial}{\partial x} (f (x)) \pm \frac{\partial}{\partial x} (g (x))

\frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (18) - \frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (y^{2})

Use \frac{\partial}{\partial x} (c) = 0 to find derivative

\frac{\partial z}{\partial x} = 0 - \frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (y^{2})

Use \frac{\partial}{\partial x} x^{n} = n x^{n - 1} to find derivative

\frac{\partial z}{\partial x} = 0 - 2 x - \frac{\partial}{\partial x} (y^{2})

Use \frac{\partial}{\partial x} (c) = 0 to find derivative

\frac{\partial z}{\partial x} = 0 - 2 x - 0

Solution

\frac{\partial z}{\partial x} = - 2 x

Function