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Question

# If $y=sec{x}^{0}$, then $\frac{dy}{dx}=$

A

$sec\left(x\right)\mathrm{tan}\left(x\right)$

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B

$sec\left({x}^{0}\right)\mathrm{tan}\left({x}^{0}\right)$

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C

$sec\left({x}^{0}\right)\mathrm{tan}\left({x}^{0}\right)\frac{\mathrm{\pi }}{180}$

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D

$sec\left({x}^{0}\right)\mathrm{tan}\left({x}^{0}\right)\frac{180}{\mathrm{\pi }}$

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Solution

## The correct option is C $sec\left({x}^{0}\right)\mathrm{tan}\left({x}^{0}\right)\frac{\mathrm{\pi }}{180}$Explanation for the correct answer:To find the value of $\frac{dy}{dx}$:Given,$y=secx°$We know,$\mathrm{\pi }$ radian $=180°$Then,$x°=\frac{\mathrm{\pi }}{180}x$So,$y=sec\frac{\mathrm{\pi }}{180}x\phantom{\rule{0ex}{0ex}}\frac{dy}{dx}=sec\left(\frac{\mathrm{\pi }}{180}x\right)\mathrm{tan}\left(\frac{\mathrm{\pi }}{180}x\right)\frac{\mathrm{\pi }}{180}\mathbf{}\mathbf{\left[}\mathbf{\because }\mathbf{}\frac{\mathbf{d}}{\mathbf{d}\mathbf{x}}\mathbf{s}\mathbf{e}\mathbf{c}\mathbf{}\mathbf{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{s}\mathbf{e}\mathbf{c}\mathbf{}\mathbf{x}\mathbf{}\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{}\mathbf{x}\mathbf{\right]}\phantom{\rule{0ex}{0ex}}\frac{dy}{dx}\mathbf{}=sec\left(x°\right)\mathrm{tan}\left(x°\right)\frac{\mathrm{\pi }}{180}$Hence, the correct option is C.

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