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

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

Evaluate

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

Solution Steps

Cancel out 2 in both numerator and denominator.

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

Multiply \frac{2x^{2}}{3y^{3}} times \frac{5y^{4}}{3x^{3}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x^{2}y^{3} in both numerator and denominator.

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

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

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

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

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

Differentiate w.r.t. x

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