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
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #27058)