导数真题100道及答案

齐狱光3111一道数学求导数的题目 -
童姣绿15661656299 ______ 先g(x)=x^(5x)两边同时取对数得:In(g(x))=5xInx,然后两边同时对x求导得:(1/g(x))g'(x)=5Inx+5,两边同乘g(x)得:g'(x)=(5Inx+5)x^(5x).

齐狱光3111一道二阶导数的题目,答案有些看不懂,求解答?问题是 设f(x)在x=x0的临近有连续的2阶导数,证明:lim(h趋近0)f(x0+h)+f(x0 - h) - 2f(x0)/h^2=f(x0)的2阶导数答... -
童姣绿15661656299 ______[答案] 因为这里的变量是h啊 对f(x0+h)+f(x0-h)-2f(x0)求导就是 f'(x0+h) (x0+h)' +f'(x0-h) (x0-h)' (f(x0)是常数,导数为0) =f'(x0+h)-f'(x0-h) f'(x0+h)-f'(x0-h)也是对h求导,所以是f''(x0+h)+f''(x0-h)

齐狱光3111(1/2)设f(x)=x(x+1)(x+2)···(x+100),求f'(0) .这道题应该用导数的定义来做,但是我算不出一...(1/2)设f(x)=x(x+1)(x+2)···(x+100),求f'(0) .这道题应... -
童姣绿15661656299 ______[答案] 很简单设g(x)=(x+1)(x+2)···(x+100) f(x)=xg(x) f'(x)=g(x)+xg'(x) f'(0)=g(0)+0*g'(x)=g(0) =1*2*3*...*100 =100!

齐狱光3111高二导数问题 在线等 12345
童姣绿15661656299 ______ f'(x)=x'(x-1)(x-2)(x-3)…(x-100)+x(x-1)'(x-2)(x-3)…(x-100)+…+x(x-1)(x-2)(x-3)…(x-100)' =(x-1)(x-2)(x-3)…(x-100)+x(x-2)(x-3)…(x-100)+…+x(x-1)(x-2)(x-3)…(x-99) 后面每项都有x,所以x=0时都等于0 所以f'(0)=(-1)(-2)(-3)……(-100)=100

齐狱光3111函数在拐点处二阶可导且导数为0. - 上学吧找答案 - 上学吧普法考试
童姣绿15661656299 ______[答案] 1. 不错,f(x)=x^2*e^(1-x),f'(x)=2x*e^(1-x)+x^2*(1-x)'*e^(1-x)=x(2-x)e^(1-x) 2. f(x)=-e^(1-x),f'(x)=-(1-x)'*e^(1-x)=e^(1-x)

齐狱光3111高中数学试题求解.急 -
童姣绿15661656299 ______ f(x)=-x^3+3x^2+9x+a f(x)的导数g(x)=-3x^2+6x+9 =(3x+3)(-x+3) =-(3x+3)(x-3)...