Solve 1/3(x^2y/2z)(2x/2z)

$$\frac{ 1 }{ 3 } ( \frac{ { x }^{ 2 } y }{ 2z } )( \frac{ 2x }{ 2z } )$$

Evaluate

$$\frac{yx^{3}}{6z^{2}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{1}{3}\times \frac{x^{2}y}{2z}\times \frac{x}{z}$$

Multiply \frac{1}{3} times \frac{x^{2}y}{2z} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{2}y}{3\times 2z}\times \frac{x}{z}$$

Multiply \frac{x^{2}y}{3\times 2z} times \frac{x}{z} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{2}yx}{3\times 2zz}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{x^{3}y}{3\times 2zz}$$

Multiply z and z to get z^{2}.

$$\frac{x^{3}y}{3\times 2z^{2}}$$

Multiply 3 and 2 to get 6.

$$\frac{x^{3}y}{6z^{2}}$$

Differentiate w.r.t. x

$$\frac{\left(\frac{x}{z}\right)^{2}y}{2}$$