First slide

Diffrentiation

Question

If $y = \tan x$ , find $\frac{d y}{d x}$ .

Easy

A

$\sin^{2} x$
B

$\cos e c^{2} x$
C

$s e c^{2} x$
D

$c o t^{2} x$

Solution

$y = \tan x = \frac{\sin x}{\cos x} \frac{d y}{d x} = \frac{\cos x \frac{d}{d x} (\sin x) - \sin x \frac{d}{d x} (\cos x)}{(\cos x)^{2}} = \frac{\cos x \cdot \cos x - \sin x (- \sin x)}{\cos^{2} x} = \frac{\cos^{2} x + \sin^{2} x}{\cos^{2} x} = \frac{1}{\cos^{2} x} = \sec^{2} x$

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