Solve 2x^2-3y^26z^2=0

Evaluate

2 x^{2} - 3 y^{2} \times 6 z^{2} = 0

Multiply the terms

2 x^{2} - 18 y^{2} z^{2} = 0

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

\frac{\partial}{\partial x} (2 x^{2} - 18 y^{2} z^{2}) = \frac{\partial}{\partial x} (0)

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} (2 x^{2}) - \frac{\partial}{\partial x} (18 y^{2} z^{2}) = \frac{\partial}{\partial x} (0)

Evaluate

More Steps

4 x - \frac{\partial}{\partial x} (18 y^{2} z^{2}) = \frac{\partial}{\partial x} (0)

Evaluate

More Steps

4 x - 36 y^{2} z \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (0)

Find the partial derivative

4 x - 36 y^{2} z \frac{\partial z}{\partial x} = 0

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

- 36 y^{2} z \frac{\partial z}{\partial x} = 0 - 4 x

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

- 36 y^{2} z \frac{\partial z}{\partial x} = - 4 x

Divide both sides

\frac{- 36 y ^{2} z \frac{\partial z}{\partial x}}{- 36 y ^{2} z} = \frac{- 4 x}{- 36 y ^{2} z}

Divide the numbers

\frac{\partial z}{\partial x} = \frac{- 4 x}{- 36 y ^{2} z}

Solution

\frac{\partial z}{\partial x} = \frac{x}{9 y ^{2} z}

Solve the equation