Solve frac{11x^{2}y}{5ac}*15a^2b/22xy^2*2xy^3/3ab^2

$$\frac { 11 x ^ { 2 } y } { 5 a c } \times \frac { 15 a ^ { 2 } b } { 22 x y ^ { 2 } } \times \frac { 2 x y ^ { 3 } } { 3 a b ^ { 2 } }$$

Evaluate

$$\frac{\left(xy\right)^{2}}{bc}$$

Solution Steps

Multiply \frac{11x^{2}y}{5ac} times \frac{15a^{2}b}{22xy^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11x^{2}y\times 15a^{2}b}{5ac\times 22xy^{2}}\times \frac{2xy^{3}}{3ab^{2}}$$

Cancel out 5\times 11axy in both numerator and denominator.

$$\frac{3abx}{2cy}\times \frac{2xy^{3}}{3ab^{2}}$$

Multiply \frac{3abx}{2cy} times \frac{2xy^{3}}{3ab^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3abx\times 2xy^{3}}{2cy\times 3ab^{2}}$$

Cancel out 2\times 3aby in both numerator and denominator.

$$\frac{xxy^{2}}{bc}$$

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

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

Differentiate w.r.t. x

$$\frac{2xy^{2}}{bc}$$