A cura di: Administrator

Calcolare la derivata della funzione

$f(x) = log frac{1 + sqrt{sin x}}{1 – sqrt{sin x}}$ $f'(x) = frac{1}{frac{1 + sqrt{sin x}}{1 – sqrt{sin x}}} cdot g[ frac{frac{1}{2 cdot sqrt{sin x}} cdot cos x cdot (1 – sqrt{sin x}) + (1 + sqrt{sin x}) cdot frac{cos x}{2 cdot sqrt{sin x}}}{(1 – sqrt{sin x})^2} g] =$ $frac{1}{1 + sqrt{sin x}} cdot frac{cos x cdot [(1 – sqrt{sin x}) + (1 + sqrt{sin x})]}{2 cdot sqrt{sin x} cdot (1 – sqrt{sin x})} =$ $frac{cos x}{sqrt{sin x} cdot (1 – sin x)}$