Solve 8y/x^2*5x^4y/4y^4

$$\frac { 8 y } { x ^ { 2 } } \cdot \frac { 5 x ^ { 4 } y } { 4 y ^ { 4 } }$$

Evaluate

$$10\times \left(\frac{x}{y}\right)^{2}$$

Solution Steps

Cancel out y in both numerator and denominator.

$$\frac{8y}{x^{2}}\times \frac{5x^{4}}{4y^{3}}$$

Multiply \frac{8y}{x^{2}} times \frac{5x^{4}}{4y^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8y\times 5x^{4}}{x^{2}\times 4y^{3}}$$

Cancel out 4yx^{2} in both numerator and denominator.

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

Multiply 2 and 5 to get 10.

$$\frac{10x^{2}}{y^{2}}$$

Differentiate w.r.t. x

$$\frac{20x}{y^{2}}$$