# If y = x sin x, finddydx

Question 36
A

cos x - x sin x

B

cos x + x sin x

C

sin x + x cos x

D

sin x - cos x.

##### Explanation

y = xsin(x)

This is a function which is in the form,

y = f(x)g(x)

It's the product of two functions and so we must make use of the product rule. This is a simple formula which you have to remember:

dy/dx = f'(x)g(x) + f(x)g'(x)

f(x) = x

g(x) = sin(x)

Therefore;

f'(x) = 1

g'(x) = cos(x)

and

dy/dx = sin(x) + xcos(x).

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