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

Evaluate

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

Find \frac{\partial z}{\partial x} by taking the derivative of both sides with respect to x

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

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

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

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

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

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

Evaluate

More Steps

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

Removing 0 doesn't change the value,so remove it from the expression

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

Swap the sides of the equation

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

Divide both sides

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

Divide the numbers

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

Solution

More Steps

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

Solve the equation