Solve x-y z=32 - ScanMath

Evaluate

x - yz = 32

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

\frac{\partial}{\partial x} (x - yz) = \frac{\partial}{\partial x} (32)

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} (x) - \frac{\partial}{\partial x} (yz) = \frac{\partial}{\partial x} (32)

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

1 - \frac{\partial}{\partial x} (yz) = \frac{\partial}{\partial x} (32)

Evaluate

More Steps

1 - y \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (32)

Find the partial derivative

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

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

- y \frac{\partial z}{\partial x} = 0 - 1

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

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

Divide both sides

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

Divide the numbers

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

Solution

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

Solve the equation