Question

find the derivative of root tan under root x?
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Answer 1

Step-by-step explanation:

Let

$y = \sqrt{ \tan( \sqrt{x} ) }$

Differentiating both sides w.r.t x, we get,

$\implies \frac{dy}{dx} = \frac{ \sec^{2} ( \sqrt{ x})}{2 \sqrt{ \tan( \sqrt{x} ) } } . \frac{1}{2 \sqrt{x} }$

$\implies \frac{dy}{dx} = \frac{ \sec^{2} ( \sqrt{ x})}{4 \sqrt{ x\tan( \sqrt{x} ) } }$