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 Answer: Option D
Explanation
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} = vfrac{delta u}{delta x} + ufrac{delta v}{delta x})
= (sin x)1 + x cos x
= sin x + x cos x
There is an explanation video available below.