Solve xy/4*2x^2/y^3

$$\frac { x y } { 4 } \times \frac { 2 x ^ { 2 } } { y ^ { 3 } }$$

Evaluate

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

Solution Steps

Multiply \frac{xy}{4} times \frac{2x^{2}}{y^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{xy\times 2x^{2}}{4y^{3}}$$

Cancel out 2y in both numerator and denominator.

$$\frac{xx^{2}}{2y^{2}}$$

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

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

Differentiate w.r.t. x

$$\frac{3\times \left(\frac{x}{y}\right)^{2}}{2}$$