How do you use the definition of a derivative to find the derivative of #-(2/3x) #?

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Answer 1 · 2017-03-09T01:02:40

#d/dx (-2/3x) = -2/3#

By definition the derivative of #f(x)# is:

#f'(x) = lim_(h->0) (f(x+h)+f(x))/h#

We have:

#f(x) = -2/3x#

#f'(x) = lim_(h->0) (-2/3(x+h) +2/3x)/h#

#f'(x) = lim_(h->0) (cancel(-2/3x)-2/3h +cancel(2/3x))/h#

#f'(x) = lim_(h->0) (-2/3 cancelh )/cancelh#

#f'(x) = -2/3#