Solve 4x^5y^4z = 88

Evaluate

4 x^{5} y^{4} z = 88

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

\frac{\partial}{\partial x} (4 x^{5} y^{4} z) = \frac{\partial}{\partial x} (88)

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} (4 x^{5} y^{4}) z + 4 x^{5} y^{4} \times \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (88)

Evaluate

More Steps

20 x^{4} y^{4} z + 4 x^{5} y^{4} \times \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (88)

Evaluate

20 z x^{4} y^{4} + 4 x^{5} y^{4} \times \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (88)

Evaluate

20 z x^{4} y^{4} + 4 x^{5} y^{4} \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (88)

Evaluate

20 z x^{4} y^{4} + 4 y^{4} x^{5} \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (88)

Find the partial derivative

20 z x^{4} y^{4} + 4 y^{4} x^{5} \frac{\partial z}{\partial x} = 0

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

4 y^{4} x^{5} \frac{\partial z}{\partial x} = 0 - 20 z x^{4} y^{4}

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

4 y^{4} x^{5} \frac{\partial z}{\partial x} = - 20 z x^{4} y^{4}

Divide both sides

\frac{4 y ^{4} x ^{5} \frac{\partial z}{\partial x}}{4 y ^{4} x ^{5}} = \frac{- 20 z x ^{4} y ^{4}}{4 y ^{4} x ^{5}}

Divide the numbers

\frac{\partial z}{\partial x} = \frac{- 20 z x ^{4} y ^{4}}{4 y ^{4} x ^{5}}

Solution

More Steps

\frac{\partial z}{\partial x} = - \frac{5 z}{x}

Solve the equation