If y x sin x find frac delta y delta x - JAMB Mathematics 2013 Question
If y = x sin x, find \(\frac{\delta y}{\delta x}\)
A
sin x - cos x
B
cos x - x sin x
C
cos x + x sin x
D
sin x + x cos x
correct option: d
y = x sin x
Where u = x and v = sin x
Then \(\frac{\delta u}{\delta x}\) = 1 and \(\frac{\delta v}{\delta x}\) = cos x
By the chain rule, \(\frac{\delta y}{\delta x} = v\frac{\delta u}{\delta x} + u\frac{\delta v}{\delta x}\)
= (sin x)1 + x cos x
= sin x + x cos x
Where u = x and v = sin x
Then \(\frac{\delta u}{\delta x}\) = 1 and \(\frac{\delta v}{\delta x}\) = cos x
By the chain rule, \(\frac{\delta y}{\delta x} = v\frac{\delta u}{\delta x} + u\frac{\delta v}{\delta x}\)
= (sin x)1 + x cos x
= sin x + x cos x
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