Solve 3x-5y^6z=25

Evaluate

3 x - 5 y^{6} z = 25

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

\frac{\partial}{\partial x} (3 x - 5 y^{6} z) = \frac{\partial}{\partial x} (25)

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} (3 x) - \frac{\partial}{\partial x} (5 y^{6} z) = \frac{\partial}{\partial x} (25)

Evaluate

More Steps

3 - \frac{\partial}{\partial x} (5 y^{6} z) = \frac{\partial}{\partial x} (25)

Evaluate

More Steps

3 - 5 y^{6} \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (25)

Find the partial derivative

3 - 5 y^{6} \frac{\partial z}{\partial x} = 0

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

- 5 y^{6} \frac{\partial z}{\partial x} = 0 - 3

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

- 5 y^{6} \frac{\partial z}{\partial x} = - 3

Divide both sides

\frac{- 5 y ^{6} \frac{\partial z}{\partial x}}{- 5 y ^{6}} = \frac{- 3}{- 5 y ^{6}}

Divide the numbers

\frac{\partial z}{\partial x} = \frac{- 3}{- 5 y ^{6}}

Solution

\frac{\partial z}{\partial x} = \frac{3}{5 y ^{6}}

Solve the equation