Solve x + 5 y + z = 10

Evaluate

x + 5 y + z = 10

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

\frac{\partial}{\partial x} (x + 5 y + z) = \frac{\partial}{\partial x} (10)

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} (x) + \frac{\partial}{\partial x} (5 y) + \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (10)

Use \frac{\partial}{\partial x} x^{n} = n x^{n - 1} to find derivative

1 + \frac{\partial}{\partial x} (5 y) + \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (10)

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

1 + 0 + \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (10)

Evaluate

1 + 0 + \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (10)

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

1 + \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (10)

Find the partial derivative

1 + \frac{\partial z}{\partial x} = 0

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

\frac{\partial z}{\partial x} = 0 - 1

Solution

\frac{\partial z}{\partial x} = - 1

Solve the equation