Solve 6x^3y^2/45y*18xy/xy^2div3y^3

$$\frac { 6 x ^ { 3 } y ^ { 2 } } { 45 y } \times \frac { 18 x y } { x y ^ { 2 } } \div 3 y ^ { 3 }$$

Evaluate

$$\frac{4\left(xy\right)^{3}}{5}$$

Solution Steps

Cancel out 3y in both numerator and denominator.

$$\frac{\frac{2yx^{3}}{15}\times \frac{18xy}{xy^{2}}}{3}y^{3}$$

Cancel out xy in both numerator and denominator.

$$\frac{\frac{2yx^{3}}{15}\times \frac{18}{y}}{3}y^{3}$$

Multiply \frac{2yx^{3}}{15} times \frac{18}{y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2yx^{3}\times 18}{15y}}{3}y^{3}$$

Cancel out 3y in both numerator and denominator.

$$\frac{\frac{2\times 6x^{3}}{5}}{3}y^{3}$$

Express \frac{\frac{2\times 6x^{3}}{5}}{3} as a single fraction.

$$\frac{2\times 6x^{3}}{5\times 3}y^{3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2\times 2x^{3}}{5}y^{3}$$

Multiply 2 and 2 to get 4.

$$\frac{4x^{3}}{5}y^{3}$$

Express \frac{4x^{3}}{5}y^{3} as a single fraction.

$$\frac{4x^{3}y^{3}}{5}$$

Differentiate w.r.t. x

$$\frac{12x^{2}y^{3}}{5}$$