Solve frac{3x^{3}y^3}{4y^2}/(4/x^2div6y/y^3)

$$\frac { 3 x ^ { 3 } y ^ { 3 } } { 4 y ^ { 2 } } / ( \frac { 4 } { x ^ { 2 } } \div \frac { 6 y } { y ^ { 3 } } )$$

Evaluate

$$\frac{9x^{5}}{8y}$$

Solution Steps

Divide \frac{3x^{3}y^{3}}{4y^{2}} by \frac{\frac{4}{x^{2}}}{\frac{6y}{y^{3}}} by multiplying \frac{3x^{3}y^{3}}{4y^{2}} by the reciprocal of \frac{\frac{4}{x^{2}}}{\frac{6y}{y^{3}}}.

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

Cancel out y in both numerator and denominator.

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

Express 3\times \frac{6}{y^{2}} as a single fraction.

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

Express 4\times \frac{4}{x^{2}} as a single fraction.

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

Multiply 3 and 6 to get 18.

$$\frac{\frac{18}{y^{2}}x^{3}y^{3}}{\frac{4\times 4}{x^{2}}y^{2}}$$

Express \frac{18}{y^{2}}x^{3} as a single fraction.

$$\frac{\frac{18x^{3}}{y^{2}}y^{3}}{\frac{4\times 4}{x^{2}}y^{2}}$$

Express \frac{18x^{3}}{y^{2}}y^{3} as a single fraction.

$$\frac{\frac{18x^{3}y^{3}}{y^{2}}}{\frac{4\times 4}{x^{2}}y^{2}}$$

Cancel out y^{2} in both numerator and denominator.

$$\frac{18yx^{3}}{\frac{4\times 4}{x^{2}}y^{2}}$$

Multiply 4 and 4 to get 16.

$$\frac{18yx^{3}}{\frac{16}{x^{2}}y^{2}}$$

Express \frac{16}{x^{2}}y^{2} as a single fraction.

$$\frac{18yx^{3}}{\frac{16y^{2}}{x^{2}}}$$

Divide 18yx^{3} by \frac{16y^{2}}{x^{2}} by multiplying 18yx^{3} by the reciprocal of \frac{16y^{2}}{x^{2}}.

$$\frac{18yx^{3}x^{2}}{16y^{2}}$$

Cancel out 2y in both numerator and denominator.

$$\frac{9x^{2}x^{3}}{8y}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{9x^{5}}{8y}$$

Differentiate w.r.t. x

$$\frac{45x^{4}}{8y}$$