Question

Sa se calculeze derivata 1 si 2 a functiei
f(x)= $e^{x} -1 -x -\frac{x^{2}} {2}$

Answer 1

$f(x) = {e}^{x} - 1 - x - \frac{ {x}^{2} }{2}$

$f'(x) = ( {e}^{x} - 1 - x - \frac{ {x}^{2} }{2} )'$

$f'(x) = {(e}^{x} )' - 1' - x' - (\frac{ {x}^{2} }{2} )'$

$f'(x) = {e}^{x} - 0 - 1 - \frac{( {x}^{2}) ' \times 2 - {x}^{2} \times 2'}{ {2}^{2} }$

$f'(x) = {e}^{x} - 1 - \frac{2x \times 2 - {x}^{2} \times 0 }{4}$

$f'(x) = {e}^{x} - 1 - \frac{4x}{4}$

$f'(x) = {e}^{x} - 1 - x$

$f''(x) = (f'(x))'$

$f''(x) = ( {e}^{x} - 1 - x)'$

$f''(x) = ( {e}^{x} )' - 1' - x'$

$f''(x) = {e}^{x} - 0 - 1$

$f''(x) = {e}^{x} - 1$