Solve z = y^2 - x^2

Simplify

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

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

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

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

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

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

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

Solution

\frac{\partial z}{\partial y} = 2 y

Function