**If \(y = x \; \mathrm{sin} \; x,\) find \(\frac{dy}{dx}\) when \(x = \frac{\pi}{2}.\)...**

### Question

If \(y = x \; \mathrm{sin} \; x,\) find \(\frac{dy}{dx}\) when \(x = \frac{\pi}{2}.\)

### Options

A) \(\frac{- \pi}{2}\)

B) \(-1\)

C) \(1\)

D) \(\frac{\pi}{2}\)

### Explanation:

\(y = x \; \mathrm{sin} \; x\)

\(\frac{dy}{dx} = 1 \times \mathrm{sin} \; x + x \; \mathrm{cos} \; x\)

\(= \mathrm{sin} \; x + x \; \mathrm{cos} \; x\)

At \(x = \frac{\pi}{2},\) \(= \mathrm{sin} \; \frac{\pi}{2} + \frac{\pi}{2} \; \mathrm{cos} \frac{π}{2}\)

\(= 1 + \frac{\pi}{2} \times (0) = 1\)

### More Past Questions:

## Dicussion (1)

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\(y = x \; \mathrm{sin} \; x\)

\(\frac{dy}{dx} = 1 \times \mathrm{sin} \; x + x \; \mathrm{cos} \; x\)

\(= \mathrm{sin} \; x + x \; \mathrm{cos} \; x\)

At \(x = \frac{\pi}{2},\) \(= \mathrm{sin} \; \frac{\pi}{2} + \frac{\pi}{2} \; \mathrm{cos} \frac{π}{2}\)

\(= 1 + \frac{\pi}{2} \times (0) = 1\)