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

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

Use the chain rule \frac{\partial}{\partial x} (f (g)) = \frac{\partial}{\partial g} (f (g)) \times \frac{\partial}{\partial x} (g) where the g = z, to find the derivative

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

Find the derivative

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

Use the commutative property to reorder the terms

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

Swap the sides of the equation

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

Divide both sides

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

Divide the numbers

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

Solution

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

Solve the equation