JAMB - Mathematics (2017 - No. 7)
If y = x Sin x, find \(\frac{dy}{dx}\) when x = \(\frac{\pi}{2}\)
\(\frac{- \pi}{2}\)
-1
1
\(\frac{ \pi}{2}\)
Explicação
y = xsinx
\(\frac{dy}{dx}\) = \(1 \sin x + x \cos x\)
= \(\sin x + x \cos x\)
At x = \(\frac{\pi}{2}\)
= sin\(\frac{\pi}{2}\) + \(\frac{\pi}{2} \cos {\frac{\pi}{2}}\)
= 1 + \(\frac{\pi}{2}\) × 0
= 1
\(\frac{dy}{dx}\) = \(1 \sin x + x \cos x\)
= \(\sin x + x \cos x\)
At x = \(\frac{\pi}{2}\)
= sin\(\frac{\pi}{2}\) + \(\frac{\pi}{2} \cos {\frac{\pi}{2}}\)
= 1 + \(\frac{\pi}{2}\) × 0
= 1