Solve 3x^3y^3z=18

Evaluate

3 x^{3} y^{3} z = 18

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

\frac{\partial}{\partial x} (3 x^{3} y^{3} z) = \frac{\partial}{\partial x} (18)

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} (3 x^{3} y^{3}) z + 3 x^{3} y^{3} \times \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (18)

Evaluate

More Steps

9 x^{2} y^{3} z + 3 x^{3} y^{3} \times \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (18)

Evaluate

9 z x^{2} y^{3} + 3 x^{3} y^{3} \times \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (18)

Evaluate

9 z x^{2} y^{3} + 3 x^{3} y^{3} \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (18)

Find the partial derivative

9 z x^{2} y^{3} + 3 x^{3} y^{3} \frac{\partial z}{\partial x} = 0

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

3 x^{3} y^{3} \frac{\partial z}{\partial x} = 0 - 9 z x^{2} y^{3}

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

3 x^{3} y^{3} \frac{\partial z}{\partial x} = - 9 z x^{2} y^{3}

Divide both sides

\frac{3 x ^{3} y ^{3} \frac{\partial z}{\partial x}}{3 x ^{3} y ^{3}} = \frac{- 9 z x ^{2} y ^{3}}{3 x ^{3} y ^{3}}

Divide the numbers

\frac{\partial z}{\partial x} = \frac{- 9 z x ^{2} y ^{3}}{3 x ^{3} y ^{3}}

Solution

More Steps

\frac{\partial z}{\partial x} = - \frac{3 z}{x}

Solve the equation