First slide

Derivatives

Question

$\frac{d}{d x} \{\frac{\sin x + \cos x}{\sqrt{1 + \sin 2 x}}\} =$

Moderate

A

0
B

1
C

2
D

3

Solution

$\frac{d}{d x} \{\frac{\sin x + \cos x}{\sqrt{1 + \sin 2 x}}\} = \frac{d}{d x} \{\frac{\sin x + \cos x}{\sqrt{\sin^{2} x + \cos^{2} x + 2 \sin x \cos x}}\} = \frac{d}{d x} \{\frac{\sin x + \cos x}{\sqrt{{(\sin x + \cos x)}^{2}}}\} = \frac{d}{d x} \{\frac{\sin x + \cos x}{\sin x + \cos x}\}$
$= \frac{d}{d x} (1) = 0.$

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