Solve 4/9xydiv3y/x

$$\frac { 4 } { 9 x y } \div \frac { 3 y } { x }$$

Evaluate

$$\frac{4}{27y^{2}}$$

Solution Steps

Divide \frac{4}{9xy} by \frac{3y}{x} by multiplying \frac{4}{9xy} by the reciprocal of \frac{3y}{x}.

$$\frac{4x}{9xy\times 3y}$$

Cancel out x in both numerator and denominator.

$$\frac{4}{3\times 9yy}$$

Multiply y and y to get y^{2}.

$$\frac{4}{3\times 9y^{2}}$$

Multiply 3 and 9 to get 27.

$$\frac{4}{27y^{2}}$$

Differentiate w.r.t. y

$$-\frac{8}{27y^{3}}$$