Question

f'(pi/4) = cos(x) - xsin(x)

Answer 1

Ok, so the derivative of cos(x)=-sin(x) and the derivative of xsin(x)=xcos(x)+sin(x) because of the product rule.

So F'(x) = -sin(x) - xcos(x) + sin(x)
Now plug in (pi/4)
F'(pi/4) = -sin(pi/4) - (pi/4)cos(pi/4) + sin(pi/4)
The sin and cos of pi/4 = sqrt(2)/2 so,
F'(pi/4) = -sqrt(2)/2 - (pi/4)(sqrt(2)/2) + sqrt(2)/2
After simplifying, you should have F'(pi/4) = -(pi)(sqrt(2)/8
Hope this helps! :)

Answer 2

thank you very much ! :)