Using the definition of the derivative function of a real variable actual value of the first derivative of function: f (x) = (x-6)/(x +3)

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embizze | High School Teacher | (Level 2) Educator Emeritus

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The formal definition of the derivative of a function is:


To find the derivative of `f(x)=(x-6)/(x+3)` :



** Common denominator for fractios and `(a/b)/h=a/(bh)` **


`=lim_(h->0)(9h)/(h(x+h+3)(x+3))`  Now let h=0



Thus `f(x)=(x-6)/(x+3)==>f'(x)=9/((x+3)^2)`



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