Solve frac{2x^{2}}{3y^{3}}*10y^2/6x^3*9x^4/4x^4

$$\frac { 2 x ^ { 2 } } { 3 y ^ { 3 } } \times \frac { 10 y ^ { 2 } } { 6 x ^ { 3 } } \times \frac { 9 x ^ { 4 } } { 4 x ^ { 4 } }$$

Evaluate

$$\frac{5}{2xy}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{2x^{2}}{3y^{3}}\times \frac{5y^{2}}{3x^{3}}\times \frac{9x^{4}}{4x^{4}}$$

Cancel out x^{4} in both numerator and denominator.

$$\frac{2x^{2}}{3y^{3}}\times \frac{5y^{2}}{3x^{3}}\times \frac{9}{4}$$

Multiply \frac{2x^{2}}{3y^{3}} times \frac{5y^{2}}{3x^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2x^{2}\times 5y^{2}}{3y^{3}\times 3x^{3}}\times \frac{9}{4}$$

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

$$\frac{2\times 5}{3\times 3xy}\times \frac{9}{4}$$

Multiply \frac{2\times 5}{3\times 3xy} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 5\times 9}{3\times 3xy\times 4}$$

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

$$\frac{5}{2xy}$$

Differentiate w.r.t. x

$$-\frac{5}{2yx^{2}}$$