First slide

Derivatives

Question

$The derivative of \sqrt{\tan x \sqrt{x}} with respect to x is$

Moderate

A

$\frac{\sin \sqrt{x}}{4 \sqrt{x} \cos \sqrt{x}}$
B

$\frac{\sec^{2} \sqrt{x}}{4 \sqrt{x} \tan \sqrt{x}}$
C

$- \frac{\sin \sqrt{x}}{4 \sqrt{x} \cos \sqrt{x}}$
D

$- \frac{\sec^{2} \sqrt{x}}{4 \sqrt{x} \tan \sqrt{x}}$

Solution

$\frac{d}{d x} [\sqrt{\tan \sqrt{x}}] = \frac{1}{2 \sqrt{\tan \sqrt{x}}} \cdot \sec^{2} \sqrt{x} \cdot \frac{1}{2 \sqrt{x}} = \frac{\sec^{2} \sqrt{x}}{4 \sqrt{x \tan \sqrt{x}}}$

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