Solve frac{5x^{3}y^{2}}{4x^{9}y^2}*8x^2y^8/10xy^6

$$\frac { 5 x ^ { 3 } y ^ { 2 } } { 4 x ^ { 9 } y ^ { 2 } } \cdot \frac { 8 x ^ { 2 } y ^ { 8 } } { 10 x y ^ { 6 } }$$

Evaluate

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

Solution Steps

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

$$\frac{5}{4x^{6}}\times \frac{8x^{2}y^{8}}{10xy^{6}}$$

Cancel out 2xy^{6} in both numerator and denominator.

$$\frac{5}{4x^{6}}\times \frac{4xy^{2}}{5}$$

Multiply \frac{5}{4x^{6}} times \frac{4xy^{2}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 4xy^{2}}{4x^{6}\times 5}$$

Cancel out 4\times 5x in both numerator and denominator.

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

Differentiate w.r.t. x

$$-\frac{5y^{2}}{x^{6}}$$