Solve 9x^5/3y^5*2y^3/5x^6

$$\frac { 9 x ^ { 5 } } { 3 y ^ { 5 } } \times \frac { 2 y ^ { 3 } } { 5 x ^ { 6 } }$$

Evaluate

$$\frac{6}{5xy^{2}}$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{3x^{5}}{y^{5}}\times \frac{2y^{3}}{5x^{6}}$$

Multiply \frac{3x^{5}}{y^{5}} times \frac{2y^{3}}{5x^{6}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3x^{5}\times 2y^{3}}{y^{5}\times 5x^{6}}$$

Cancel out y^{3}x^{5} in both numerator and denominator.

$$\frac{2\times 3}{5xy^{2}}$$

Multiply 2 and 3 to get 6.

$$\frac{6}{5xy^{2}}$$

Differentiate w.r.t. x

$$-\frac{6}{5\left(xy\right)^{2}}$$