Solve 2x = z^2 - y^2

Evaluate

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

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

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

Use differentiation rule \frac{\partial}{\partial x} (c f (x)) = c \times \frac{\partial}{\partial x} (f (x))

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

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

2 \times 1 = \frac{\partial}{\partial x} (z^{2} - y^{2})

Multiply the terms

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

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

Evaluate

More Steps

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

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

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

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

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

Swap the sides of the equation

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

Divide both sides

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

Divide the numbers

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

Solution

\frac{\partial z}{\partial x} = \frac{1}{z}

Solve the equation