Solve x y z=30 - ScanMath

Evaluate

x yz = 30

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} (30)

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

\frac{\partial}{\partial x} (x y) z + x y \times \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (30)

Evaluate

More Steps

yz + x y \times \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (30)

Evaluate

yz + x y \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (30)

Find the partial derivative

yz + x y \frac{\partial z}{\partial x} = 0

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

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

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

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

Divide both sides

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

Divide the numbers

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

Solution

More Steps

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

Solve the equation