Is the following true or false? the third derivative of the quantity x times the sine of x equals the product of negative x and the cosine of x minus 3 times the sine of x True False

Answer 1

If f(x)=xsin(x)

First derivative is xcos(x) +sin(x)

Second derivative is x[-sin(x)] + cos(x) + cos(x) = -xsin(x) + 2cos(x)

Third Derivative is -x[cos(x)] -sin(x) -2sin(x) = -xcos(x) - 3sin(x)

Yes answer is TRUE