Solve x*y=z y - ScanMath

Evaluate

x y = zy

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

\frac{\partial}{\partial x} (x y) = \frac{\partial}{\partial x} (zy)

Use differentiation rule \frac{\partial}{\partial x} (c f (x)) = c \times \frac{\partial}{\partial x} (f (x))

y \times \frac{\partial}{\partial x} (x) = \frac{\partial}{\partial x} (zy)

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

y \times 1 = \frac{\partial}{\partial x} (zy)

Multiply the terms

y = \frac{\partial}{\partial x} (zy)

Use differentiation rule \frac{\partial}{\partial x} (c f (x)) = c \times \frac{\partial}{\partial x} (f (x))

y = y \times \frac{\partial}{\partial x} (z)

Find the derivative

y = y \frac{\partial z}{\partial x}

Swap the sides of the equation

y \frac{\partial z}{\partial x} = y

Divide both sides

\frac{y \frac{\partial z}{\partial x}}{y} = \frac{y}{y}

Divide the numbers

\frac{\partial z}{\partial x} = \frac{y}{y}

Solution

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

Solve the equation