If y x sinx find frac dy dx - JAMB Mathematics 2010 Question
If y = x sinx, find \(\frac{dy}{dx}\)
A
sin x - x cosx
B
sinx + x cosx
C
sinx - cosx
D
sinx + cosx
correct option: b
If y = x sinx, then
Let u = x and v = sinx
(\frac{du}{dx}) = 1 and (\frac{dv}{dx}) = cosx
Hence by the product rule,
(\frac{dy}{dx}) = v (\frac{du}{dx}) + u(\frac{dv}{dx})
= (sin x) x 1 + x cosx
= sinx + x cosx
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