Exponential and trigonometric functions, question 22

A student finds $y'\!\left(\tfrac{\pi}{2}\right)$ for the function below as shown. Find the first line that is wrong.

y = x\cos x

$y' = 1\cdot\cos x + x\cdot\sin x$
Product rule: the derivative of x times cos x, plus x times the derivative of cos x.
$y'\!\left(\tfrac{\pi}{2}\right) = \cos\tfrac{\pi}{2} + \tfrac{\pi}{2}\sin\tfrac{\pi}{2}$
Substitute x = π/2.
$= 0 + \tfrac{\pi}{2} = \tfrac{\pi}{2}$
cos(π/2) = 0 and sin(π/2) = 1.

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