Solve x^2y/4xy*x/6*3y^5/x^4

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

Evaluate

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

Solution Steps

Cancel out xy in both numerator and denominator.

$$\frac{x}{4}\times \frac{x}{6}\times \frac{3y^{5}}{x^{4}}$$

Multiply \frac{x}{4} times \frac{x}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{xx}{4\times 6}\times \frac{3y^{5}}{x^{4}}$$

Multiply \frac{xx}{4\times 6} times \frac{3y^{5}}{x^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{xx\times 3y^{5}}{4\times 6x^{4}}$$

Cancel out 3xx in both numerator and denominator.

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

Multiply 2 and 4 to get 8.

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

Differentiate w.r.t. x

$$-\frac{y^{5}}{4x^{3}}$$