Solve z^2 - x^2 = y^21

Evaluate

z^{2} - x^{2} = y^{2} \times 1

Any expression multiplied by 1 remains the same

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

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

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

Evaluate

More Steps

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

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

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

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

Move the expression to the right-hand side and change its sign

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

Add the terms

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

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

Solve the equation