Solve (x^3y/4)div(4/xdiv6/y^3)

$$( \frac { x ^ { 3 } y } { 4 } ) \div ( \frac { 4 } { x } \div \frac { 6 } { y ^ { 3 } } )$$

Evaluate

$$\frac{3x^{4}}{8y^{2}}$$

Solution Steps

Divide \frac{x^{3}y}{4} by \frac{\frac{4}{x}}{\frac{6}{y^{3}}} by multiplying \frac{x^{3}y}{4} by the reciprocal of \frac{\frac{4}{x}}{\frac{6}{y^{3}}}.

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

Express x^{3}\times \frac{6}{y^{3}} as a single fraction.

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

Express 4\times \frac{4}{x} as a single fraction.

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

Express \frac{x^{3}\times 6}{y^{3}}y as a single fraction.

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

Cancel out y in both numerator and denominator.

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

Multiply 4 and 4 to get 16.

$$\frac{\frac{6x^{3}}{y^{2}}}{\frac{16}{x}}$$

Divide \frac{6x^{3}}{y^{2}} by \frac{16}{x} by multiplying \frac{6x^{3}}{y^{2}} by the reciprocal of \frac{16}{x}.

$$\frac{6x^{3}x}{y^{2}\times 16}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3xx^{3}}{8y^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{3x^{4}}{8y^{2}}$$

Differentiate w.r.t. x

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