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Differentiate w.r.t. x
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\frac{\left(x^{-6}\right)^{-\frac{1}{2}}}{\left(9y^{-4}\right)^{-\frac{1}{2}}}
To raise \frac{x^{-6}}{9y^{-4}} to a power, raise both numerator and denominator to the power and then divide.
\frac{x^{3}}{\left(9y^{-4}\right)^{-\frac{1}{2}}}
To raise a power to another power, multiply the exponents. Multiply -6 and -\frac{1}{2} to get 3.
\frac{x^{3}}{9^{-\frac{1}{2}}\left(y^{-4}\right)^{-\frac{1}{2}}}
Expand \left(9y^{-4}\right)^{-\frac{1}{2}}.
\frac{x^{3}}{9^{-\frac{1}{2}}y^{2}}
To raise a power to another power, multiply the exponents. Multiply -4 and -\frac{1}{2} to get 2.
\frac{x^{3}}{\frac{1}{3}y^{2}}
Calculate 9 to the power of -\frac{1}{2} and get \frac{1}{3}.