Explicație pas cu pas:
[tex]f(x) = ( {x}^{2} - 5x + 7) \times {e}^{x} [/tex]
[tex]f'(x) = \left( ( {x}^{2} - 5x + 7) \times {e}^{x}\right)' \\[/tex]
[tex]= ( {x}^{2} - 5x + 7)' {e}^{x} + ({e}^{x})'( {x}^{2} - 5x + 7) \\ [/tex]
[tex]= (2x - 5){e}^{x} + {e}^{x}( {x}^{2} - 5x + 7) \\[/tex]
[tex]= {e}^{x}( {x}^{2} - 3x + 2) \\[/tex]
[tex]= {e}^{x}(x - 1)(x - 2)[/tex]
