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Question

Derivative of f(x)=xsin(x) is


Your Answer
A
cos(x)2x+sin(x)
Your Answer
B
x.cos(x)2sin(x)
Correct Answer
C
x.cos(x)2+sin(x)
Your Answer
D
cos(x)2xsin(x)

Solution

The correct option is C x.cos(x)2+sin(x)
Given, f(x)=xsin(x)
So, derivative of the given function is
df(x)dx=d(xsin(x))dx
Using product and chain rule together we get
xdsin(x)dx+sin(x)dxdx
 x[dsin(x)dx×dxdx]+sin(x)
 x(cos(x)2x)+sin(x)
 x.cos(x)2+sin(x)

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