Differentiate the following functions with respect to x: 5x^ - Vidyadip

Question

Differentiate the following functions with respect to x:
$\tan5\text{x}^\circ$

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Answer

Let, $\text{y}=\tan5\text{x}^\circ$
$\Rightarrow\ \text{y}=\tan\Big(5\text{x}\times\frac{\pi}{180}\Big)$
Differentiate it with respect to x we get,
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\tan\Big(5\text{x}\times\frac{\pi}{180}\Big)$
$=\sec^2\Big(5\text{x}\times\frac{\pi}{180}\Big)\frac{\text{d}}{\text{dx}}\Big(5\text{x}\times\frac{\pi}{108}\Big) $
[Using chain rule]
$=\Big(\frac{5\text{x}}{180}\Big)\sec^2\Big(5\text{x}\times\frac{\pi}{180}\Big)$
$=\frac{5\pi}{180}\sec^2(5\text{x}^\circ)$
Hence, $\frac{\text{d}}{\text{dx}}(\tan5\text{x}^\circ)=\frac{5\pi}{180}\sec^2(5\text{x}^\circ)$

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