Solve (x^3/10)(5y^2/6x^5)

$$( \frac { x ^ { 3 } } { 10 } ) ( \frac { 5 y ^ { 2 } } { 6 x ^ { 5 } } )$$

Evaluate

$$\frac{\left(\frac{y}{x}\right)^{2}}{12}$$

Solution Steps

Multiply \frac{x^{3}}{10} times \frac{5y^{2}}{6x^{5}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{3}\times 5y^{2}}{10\times 6x^{5}}$$

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

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

Multiply 2 and 6 to get 12.

$$\frac{y^{2}}{12x^{2}}$$

Differentiate w.r.t. x

$$-\frac{y^{2}}{6x^{3}}$$