Solve 4x-2y-3z^4=3

Evaluate

4 x - 2 y - 3 z^{4} = 3

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

\frac{\partial}{\partial x} (4 x - 2 y - 3 z^{4}) = \frac{\partial}{\partial x} (3)

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} (4 x) - \frac{\partial}{\partial x} (2 y) - \frac{\partial}{\partial x} (3 z^{4}) = \frac{\partial}{\partial x} (3)

Evaluate

More Steps

4 - \frac{\partial}{\partial x} (2 y) - \frac{\partial}{\partial x} (3 z^{4}) = \frac{\partial}{\partial x} (3)

Use \frac{\partial}{\partial x} (c) = 0 to find derivative

4 - 0 - \frac{\partial}{\partial x} (3 z^{4}) = \frac{\partial}{\partial x} (3)

Evaluate

More Steps

4 - 0 - 12 z^{3} \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (3)

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

4 - 12 z^{3} \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (3)

Find the partial derivative

4 - 12 z^{3} \frac{\partial z}{\partial x} = 0

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

- 12 z^{3} \frac{\partial z}{\partial x} = 0 - 4

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

- 12 z^{3} \frac{\partial z}{\partial x} = - 4

Divide both sides

\frac{- 12 z ^{3} \frac{\partial z}{\partial x}}{- 12 z ^{3}} = \frac{- 4}{- 12 z ^{3}}

Divide the numbers

\frac{\partial z}{\partial x} = \frac{- 4}{- 12 z ^{3}}

Solution

\frac{\partial z}{\partial x} = \frac{1}{3 z ^{3}}

Solve the equation