Solve frac{sqrt[3]{x}*sqrt[4]{y}*sqrt{x}*sqrt[5]{y}}{sqrt[4]{x}sqrt[3]{y}}

$$\frac { \sqrt[ 3 ] { x } \cdot \sqrt[ 4 ] { y } \cdot \sqrt { x } \cdot \sqrt[ 5 ] { y } } { \sqrt[ 4 ] { x } \sqrt[ 3 ] { y } }$$

Evaluate

$$y^{\frac{7}{60}}x^{\frac{7}{12}}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\sqrt[5]{y}\sqrt[4]{y}\sqrt[3]{x}\sqrt{x}}{\sqrt[4]{x}\sqrt[3]{y}}$$

Cancel out y^{\frac{2}{15}}\sqrt[5]{y}\sqrt[4]{x} in both numerator and denominator.

$$\sqrt[12]{x}y^{\frac{7}{60}}\sqrt{x}$$

Expand the expression.

$$y^{\frac{7}{60}}x^{\frac{7}{12}}$$

Differentiate w.r.t. x

$$\frac{7y^{\frac{7}{60}}}{12x^{\frac{5}{12}}}$$