Solve 4y^3z=10x - ScanMath

Evaluate

4 y^{3} z = 10 x

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

\frac{\partial}{\partial x} (4 y^{3} z) = \frac{\partial}{\partial x} (10 x)

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

4 y^{3} \times \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (10 x)

Find the derivative

4 y^{3} \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (10 x)

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

4 y^{3} \frac{\partial z}{\partial x} = 10 \times \frac{\partial}{\partial x} (x)

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

4 y^{3} \frac{\partial z}{\partial x} = 10 \times 1

Multiply the terms

4 y^{3} \frac{\partial z}{\partial x} = 10

Divide both sides

\frac{4 y ^{3} \frac{\partial z}{\partial x}}{4 y ^{3}} = \frac{10}{4 y ^{3}}

Divide the numbers

\frac{\partial z}{\partial x} = \frac{10}{4 y ^{3}}

Solution

\frac{\partial z}{\partial x} = \frac{5}{2 y ^{3}}

Solve the equation