The differential coefficient of \( a^{\log _{10} \operatorname{cosec}^{-1} x} \), is....
The differential coefficient of \( a^{\log _{10} \operatorname{cosec}^{-1} x} \), is
\( \mathrm{P} \)
(1) \( \frac{a^{\log _{10}\left(\operatorname{cosec}^{-1} x\right)}}{\operatorname{cosec}^{-1} x} \cdot \frac{1}{x \sqrt{x^{2}-1}} \log _{10} a \)
(2) \( -\frac{a^{\log _{10}\left(\operatorname{cosec}^{-1} x\right)}}{\operatorname{cosec}^{-1} x} \cdot \frac{1}{|x| \sqrt{x^{2}-1}} \log _{10} a \)
(3) \( -\frac{a^{\log _{10}\left(\operatorname{cosec}^{-1} x\right)}}{\operatorname{cosec}^{-1} x} \cdot \frac{1}{|x| \sqrt{x^{2}}-1} \log _{a} 10 \)
(4) \( \frac{a^{\log _{10} \operatorname{cosec}^{-1} x}}{\operatorname{cosec}^{-1} x} \cdot \frac{1}{x \sqrt{x^{2}-1}} \log _{a} 10 \)
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