use the formal definition to find the derivative of f(x)=1/(x+1) for x (not equal to) -1?

2014-07-09 6:12 am
please show steps and explain.

回答 (1)

2014-07-15 2:43 am
f '(x) = lim(h-->0) [f(x+h) - f(x)]/h
........= lim(h-->0) [1/(x+h+1) - 1/(x+1)]/h
........= lim(h-->0) [1/(x+h+1) - 1/(x+1)] * (1/h)
........= lim(h-->0) [((x+1) - (x+h+1)) / ((x+h+1)(x+1))] * (1/h)
........= lim(h-->0) [-h/((x+h+1)(x+1))] * (1/h)
........= lim(h-->0) -1/((x+h+1)(x+1))
........= -1/((x+0+1)(x+1))
........= -1/(x+1)^2.

I hope this helps!


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