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How do you find f'(x) using the definition of a derivative for #-(2/3x) #?

1 Answer

Feb 25, 2016

Evaluate the limit to find that

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

Explanation:

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

we have

#d/dx(-2/3x) = lim_(h->0)(-2/3(x+h)-(-2/3x))/h#

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

#=lim_(h->0)-2/3*h/h#

#=lim_(h->0)-2/3#

#=-2/3#

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