Question

$f(x)= frac{10x+1}{ sqrt{4 x^{2} +1}}$ Вычислить f(1)

Answer 1

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