Question

Ma poate ajuta cineva?​

Answer 1

$f`(x) = (\sqrt{x+2} )`$ notezi pe x+2 = t avand in vedere ca e o derivata compusa

$f`(x) = (\sqrt{t})` * t` = \frac{1}{2\sqrt{t} } * (x+2)` =\frac{1}{2\sqrt{x+2} }$

$\int\limits^2_1 {\frac{1}{2\sqrt{x+2} } } \, dx = \frac{1}{2}\int\limits^2_1 {\frac{1}{2\sqrt{x+2} } } \, dx = \frac{1}{2} \int\limits^2_1 {\frac{1}{\sqrt{t} } } \, dx = \frac{1}{2} * 2\sqrt{t} |^{2}_{1} = \sqrt{x+2} |^{2}_{1} = \sqrt{4} - \sqrt{3}$