How do you find f'(x) using the definition of a derivative for $- (\frac{2}{3} x)$ $-(2/3x)$ ?

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Answer 1 · 2016-02-25T01:30:27

Evaluate the limit to find that

$\frac{d}{d x} (- \frac{2}{3} x) = - \frac{2}{3}$ $d/dx(-2/3x)=-2/3$

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

we have

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

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

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

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

$=-2/3$

How do you find f'(x) using the definition of a derivative for -(2/3x) −(23x)-(2/3x) ?