[latex]f(x)= \frac{10x+1}{ \sqrt{4 x^{2} +1}} [/latex] Вычислить f(1)

[latex]f(x)= \frac{10x+1}{\sqrt{4x^2+1}} \\\\f'(x)= \frac{10\cdot \sqrt{4x^2+1}-(10x+1)\cdot \frac{8x}{2\sqrt{4x^2+1}}}{4x^2+1} = \frac{10\cdot (4x^2+1)-4x(10x+1)}{(4x^2+1)\sqrt{4x^2+1}} \\\\f'(1)= \frac{10\cdot 5-4\cdot 11}{5\sqrt5}= \frac{6}{5\sqrt5} = \frac{6\sqrt5}{25} [/latex]