Question

If f(x) = x sin x, then `f^'(π/2)` is equal to ______.

Options

• 0

• 1

• –1

• `1/2`

Answer 1

If f(x) = x sin x, then `f^'(π/2)` is equal to 1.

Explanation:

∵ f(x) = x sin x

`\implies` f'(x) = `d/(dx) (x sin x)`

= `sin x d/(dx) x + x d/(dx) sin x`

= sin x + x cos x

`\implies f^'(π/2) = sin  π/2 + π/2 cos  π/2` = 1