Differentiate the functions with respect to x. ( ( x )) - Vidyadip

Question

Differentiate the functions with respect to x.
$\sec(\tan(\sqrt{\text{x}}))$

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Answer

$\text{Let y} = \sec(\tan\sqrt{\text{x}})$
$\therefore \frac{\text{dy}}{\text{dx}} = \sec(\tan\sqrt{\text{x}})\tan(\tan\sqrt{\text{x}})\frac{\text{d}}{\text{dx}}(\tan\sqrt{\text{x}})$
$= \sec(\tan\sqrt{\text{x}})\tan(\tan\sqrt{\text{x}})\sec^{2}\sqrt{\text x}\frac{\text{d}}{\text{dx}}\sqrt{\text{x}}$
$= \sec(\tan\sqrt{\text{x}})\tan(\tan\sqrt{\text{x}})\sec^{2}\sqrt{\text x}.\frac{1}{2}\text{x}^{\frac{1}{2}-1}$
$= \sec(\tan\sqrt{\text{x}})\tan(\tan\sqrt{\text{x}})\sec^{2}\sqrt{\text x}.\frac{1}{2\sqrt{\text{x}}}$

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