Solve -3xydiv2y/3x3x/2y

$$-3xy \div \frac{ 2y }{ 3x } \frac{ 3x }{ 2y }$$

Evaluate

$$-\frac{27x^{3}}{4y}$$

Solution Steps

Divide -3xy by \frac{2y}{3x} by multiplying -3xy by the reciprocal of \frac{2y}{3x}.

$$\frac{-3xy\times 3x}{2y}\times \frac{3x}{2y}$$

Cancel out y in both numerator and denominator.

$$\frac{-3\times 3xx}{2}\times \frac{3x}{2y}$$

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

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

Multiply -3 and 3 to get -9.

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

Multiply \frac{-9x^{2}}{2} times \frac{3x}{2y} by multiplying numerator times numerator and denominator times denominator.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Multiply -9 and 3 to get -27.

$$\frac{-27x^{3}}{2\times 2y}$$

Multiply 2 and 2 to get 4.

$$\frac{-27x^{3}}{4y}$$

Differentiate w.r.t. x

$$-\frac{81x^{2}}{4y}$$