Найти значение производное f(x)=4sinx-coax при x=-pi/4

[latex]f'(x)=(4\sin x-\cos x)'=4\cos x+\sin x \Longrightarrow\\\\ 4\cos ( -\frac{\pi}{4} )+\sin (- \frac{\pi}{4} )=2\sqrt2- \frac{1}{\sqrt2} = \frac{3}{\sqrt2}= \frac{3\sqrt2}{2} [/latex]

[latex] f(x) = 4 \sin{x} - \cos{x} \ ; [/latex] [latex] f'(x) = ( 4 \sin{x} - \cos{x} )' = 4 ( \sin{x} )' - ( \cos{x} )' = 4 \cos{x} - ( - \sin{x} ) \ ; [/latex] [latex] f'(x) = 4 \cos{x} + \sin{x} \ ; [/latex] [latex] f'( x = -\frac{ \pi }{4} ) = 4 \cos{ ( -\frac{ \pi }{4} ) } + \sin{ ( -\frac{ \pi }{4} ) } = 4 \cdot \frac{ \sqrt{2} }{2} - \frac{ \sqrt{2} }{2} = 3 \cdot \frac{ \sqrt{2} }{2} \ ; [/latex] О т в е т :    [latex] f'( x = -\frac{ \pi }{4} ) = \frac{3}{2} \sqrt{2} \ . [/latex]