Solve x-6y^2z=5 - Socratic AI (ScanMath)

Evaluate

x - 6 y^{2} z = 5

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

\frac{\partial}{\partial x} (x - 6 y^{2} z) = \frac{\partial}{\partial x} (5)

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} (6 y^{2} z) = \frac{\partial}{\partial x} (5)

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

1 - \frac{\partial}{\partial x} (6 y^{2} z) = \frac{\partial}{\partial x} (5)

Evaluate

More Steps

1 - 6 y^{2} \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (5)

Find the partial derivative

1 - 6 y^{2} \frac{\partial z}{\partial x} = 0

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

- 6 y^{2} \frac{\partial z}{\partial x} = 0 - 1

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

- 6 y^{2} \frac{\partial z}{\partial x} = - 1

Divide both sides

\frac{- 6 y ^{2} \frac{\partial z}{\partial x}}{- 6 y ^{2}} = \frac{- 1}{- 6 y ^{2}}

Divide the numbers

\frac{\partial z}{\partial x} = \frac{- 1}{- 6 y ^{2}}

Solution

\frac{\partial z}{\partial x} = \frac{1}{6 y ^{2}}

X 6y^2z=5