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Differentiate w.r.t. x
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\frac{x^{3}y\times \left(\frac{6}{y^{3}}\right)}{4\times \left(\frac{4}{x}\right)}
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{\frac{x^{3}\times 6}{y^{3}}y}{4\times \left(\frac{4}{x}\right)}
Express x^{3}\times \left(\frac{6}{y^{3}}\right) as a single fraction.
\frac{\frac{x^{3}\times 6}{y^{3}}y}{\frac{4\times 4}{x}}
Express 4\times \left(\frac{4}{x}\right) as a single fraction.
\frac{\frac{x^{3}\times 6y}{y^{3}}}{\frac{4\times 4}{x}}
Express \frac{x^{3}\times 6}{y^{3}}y as a single fraction.
\frac{\frac{6x^{3}}{y^{2}}}{\frac{4\times 4}{x}}
Cancel out y in both numerator and denominator.
\frac{\frac{6x^{3}}{y^{2}}}{\frac{16}{x}}
Multiply 4 and 4 to get 16.
\frac{6x^{3}x}{y^{2}\times 16}
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{3xx^{3}}{8y^{2}}
Cancel out 2 in both numerator and denominator.
\frac{3x^{4}}{8y^{2}}
To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.