题目
f(x) = (3)/(5-x) + (x^2)/(5),则 f'(2) = ____,如果答案为分数,写作a/b的形式。
$f(x) = \frac{3}{5-x} + \frac{x^2}{5}$,则 $f'(2) = \_\_\_\_$,如果答案为分数,写作a/b的形式。
题目解答
答案
对函数 $ f(x) = \frac{3}{5-x} + \frac{x^2}{5} $ 求导,得
$f'(x) = \frac{3}{(5-x)^2} + \frac{2x}{5}$
代入 $ x = 2 $,得
$f'(2) = \frac{3}{(5-2)^2} + \frac{2 \times 2}{5} = \frac{3}{9} + \frac{4}{5} = \frac{1}{3} + \frac{4}{5} = \frac{5}{15} + \frac{12}{15} = \frac{17}{15}$
答案: $\boxed{\frac{17}{15}}$