Помогите пожалуйста ! 1. Найти [latex]1) f' (x) ; f' (-1):f(x)=x^3-3x^2+5x+3 [/latex] [latex]2) f'(x);f'(0):f(x)=e^x \cdot cosx[/latex] [latex]3)f'(x);f'(4):f(x)=\frac{x^2+2}{x-3}[/latex] [latex]4)f'(x);f'(16):f(x)=\sqrt[4]{x}[...

1) [latex]f(x)=x^3-3x^2+5x+3[/latex] [latex]f'(x)=3x^2-6x+5[/latex] [latex]f'(-1)=3+6+5=14[/latex] 2) [latex]f(x)=e^xcosx[/latex] [latex]f'(x)=e^xcosx-e^xsinx[/latex] [latex]f'(0)=e^0cos0-e^0sin0=1[/latex] 3)[latex]f(x)=\frac{x^2+2}{x-3}[/latex] [latex]f'(x)=\frac{2x(x-3)-(x^2+2)*1}{(x-3)^2}=\frac{x^2-6x-2}{(x-3)^2}[/latex] [latex]f'(4)=\frac{16-24-2}{1}=-10[/latex] 4) [latex]f(x)=\sqrt[4]{x}[/latex] [latex]f'(x)=\frac14 x^{-\frac34}[/latex] [latex]f'(16)=\frac14 16^{-\frac34}=\frac{1}{4*2^3}=\frac{1}{32}[/latex] 5) [latex]y=(4x-11)^{11}[/latex] [latex]y'=11(4x-11)^{10}*4=44(4x-11)^{10}[/latex] 6)[latex]y=sin(3x+2)[/latex] [latex]y'=3cos(3x+2)[/latex] 7)[latex]y=cos(2x-3)[/latex] [latex]y'=-2sin(2x-3)[/latex] 8)[latex]y=tg(5x+6)[/latex] [latex]y'=-\frac{5}{cos^2(5x+6)}[/latex] 9)[latex]y=ctg(4x-3)[/latex] [latex]y'=\frac{4}{sin^2(4x-3)}[/latex] 10)[latex]y=e^{4x-5}[/latex] [latex]y'=4e^{4x-5}[/latex] 11)[latex]y=5^{3x+2}[/latex] [latex]y'=\frac{3}{ln5}*5^{3x+2}[/latex] 12)[latex]y=log_7(8x-3)[/latex] [latex]y'=\frac{1}{ln7}*\frac{8}{8x-3}[/latex] 13)[latex]y=ln(3x+4)[/latex] [latex]y'=\frac{3}{3x+4}[/latex] 14)[latex]f(x)=\sqrt{-x^2+6x+11}[/latex] [latex]f'(x)=\frac{-2x+6}{2\sqrt{-x^2+6x+11}}[/latex] [latex]f'(1)=\frac{-2+6}{2\sqrt{-1+6+11}}=\frac{-4}{2\sqrt{16}}=\frac12[/latex] 15)[latex]f(x)=(5-x)\sqrt(4-2x)[/latex] [latex]f'(x)=-\sqrt{4-2x-\frac{2(5-x)}{2\sqrt{4-2x}}[/latex] [latex]f'(0)=-2-\frac{10}{4}=2-\frac52=-\frac12[/latex] 16)[latex]f(x)=\frac{\sqrt{x^2-9}}{x-4}[/latex] [latex]f'(x)=\frac{\frac{x}{\sqrt{x^2-9}}*(x-4)-\sqrt{x^2-9}}{(x-4)^2}[/latex] [latex]f'(5)=\frac{\frac{5}{4}*1-4}{1}=16[/latex]