Solve 2x - 2y z = -2

Evaluate

2 x - 2 yz = - 2

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

\frac{\partial}{\partial x} (2 x - 2 yz) = \frac{\partial}{\partial x} (- 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} (2 x) - \frac{\partial}{\partial x} (2 yz) = \frac{\partial}{\partial x} (- 2)

Evaluate

More Steps

2 - \frac{\partial}{\partial x} (2 yz) = \frac{\partial}{\partial x} (- 2)

Evaluate

More Steps

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

Find the partial derivative

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

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

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

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

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

Divide both sides

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

Divide the numbers

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

Solution

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

Solve the equation