What is the value of ddx ( ⁡ x ⁡ x)? - Vidyadip

MCQ

What is the value of $\text{ddx} (\sin⁡ x \tan⁡ x)?$

✓
$\sin⁡ x + \tan⁡ x \sec⁡ x$
B
$\cos⁡ x + \tan⁡ x \sec⁡ x$
C
$\sin⁡ x + \tan⁡ x$
D
$\sin⁡ x + \tan⁡ x \sec^2x$

✓

Answer

Correct option: A.

$\sin⁡ x + \tan⁡ x \sec⁡ x$

We follow product rule $\frac{\text{d}}{\text{dx}}(\text{f}.\text{g})=\text{g.}\frac{\text{d}}{\text{dx}}(\text{f})+(\text{f})\frac{\text{d}}{\text{dx}}(\text{f}.\text{g})$
Here, $f = \sin⁡ x$ and $g = \tan⁡ x$
$\frac{\text{d}}{\text{dx}} (\sin⁡ x \tan⁡ x) = \cos⁡ x \tan⁡ x + \sec^2 x \sin x$
$\frac{\text{d}}{\text{dx}} (\sin⁡ x \tan⁡ x) = \sin⁡ x + \tan⁡ x \sec⁡ x$

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