Solve frac{11x^{2}y}{5x^{9}c}*15a^2b/22xy^2*2xy^3/3ab^2

$$\frac { 11 x ^ { 2 } y } { 5 x ^ { 9 } c } \times \frac { 15 a ^ { 2 } b } { 22 x y ^ { 2 } } \times \frac { 2 x y ^ { 3 } } { 3 a b ^ { 2 } }$$

Evaluate

$$\frac{ay^{2}}{bcx^{7}}$$

Solution Steps

Cancel out x^{2} in both numerator and denominator.

$$\frac{11y}{5cx^{7}}\times \frac{15a^{2}b}{22xy^{2}}\times \frac{2xy^{3}}{3ab^{2}}$$

Multiply \frac{11y}{5cx^{7}} times \frac{15a^{2}b}{22xy^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11y\times 15a^{2}b}{5cx^{7}\times 22xy^{2}}\times \frac{2xy^{3}}{3ab^{2}}$$

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

$$\frac{3ba^{2}}{2cxyx^{7}}\times \frac{2xy^{3}}{3ab^{2}}$$

Multiply \frac{3ba^{2}}{2cxyx^{7}} times \frac{2xy^{3}}{3ab^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3ba^{2}\times 2xy^{3}}{2cxyx^{7}\times 3ab^{2}}$$

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

$$\frac{ay^{2}}{bcx^{7}}$$

Differentiate w.r.t. x

$$-\frac{7ay^{2}}{bcx^{8}}$$