Solve 2x^2y^3/9div8x^3y/3

$$\frac { 2 x ^ { 2 } y ^ { 3 } } { 9 } \div \frac { 8 x ^ { 3 } y } { 3 }$$

Evaluate

$$\frac{y^{2}}{12x}$$

Solution Steps

Divide \frac{2x^{2}y^{3}}{9} by \frac{8x^{3}y}{3} by multiplying \frac{2x^{2}y^{3}}{9} by the reciprocal of \frac{8x^{3}y}{3}.

$$\frac{2x^{2}y^{3}\times 3}{9\times 8x^{3}y}$$

Cancel out 2\times 3yx^{2} in both numerator and denominator.

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

Multiply 3 and 4 to get 12.

$$\frac{y^{2}}{12x}$$

Differentiate w.r.t. x

$$-\frac{\left(\frac{y}{x}\right)^{2}}{12}$$