Consider the following for the next items that follow:

Let a function f be defined on ℝ - {0} and $\rm 2 f(x)+f\left(\frac{1}{x}\right)=x+3 $.

If f is differentiable, then what is f'(0.5) equal to?

If f(x) = |ln|x|| where 0 < x < 1, then what is f'(0.5) equal to ?

If f'(x) = cos (In x) and $y=f\left(\frac{2 x-3}{x}\right)$, then what is $\frac{d y}{d x}$ equal to ?

Consider the following for the next three (03) items that follow :

Let f(x) = Pe^x + Qe^2x + Re^3x where P, Q, R are real numbers. Further f(0) = 6, f'(ln 3) = 282 and $\int_0^{\ln 2} f(x) d x=11$

What is f'(0) equal to ?