Ask for advice on math problems. High school derivative and its application. I want this process
1. Derive both sides of the equation and get F' (x) = 2xf' (π/3)+COSX. Let x=π/3, and we get F' (π/3) = 2π/3f' (π/3)+COSπ/3, that is, F' (π/3).
2. Derivation, f' (x) = sinx+xcosx, f(π/2)=π/2+ 1, f'(π/2)= 1, because the tangent is perpendicular to the straight line, the slope of the straight line =-1.