Find f '(t) using the definition of derivative. `f(t) = (2t + 1)/(t+3)` My algebra is not coming out like in the back of the book.   

Expert Answers
lemjay eNotes educator| Certified Educator


The derivative of this function with respect to t can determined using the definition of derivative which is:

`f'(t)=lim_(h->0) (f(t+h)-f(t))/h`

To apply this formula,  evaluate the given function at t=t+h to get f(t+h).




Then, plug-in this to the formula of above.


Before taking the limit, simplify the complex fraction. To do so, multiply the top and bottom by the LCD which is (t+h+3)(t+3).




To simplify the numerator, apply distributive property. And combine like terms.





Then, cancel common factor which is h.




Now that it is in simplified form, proceed to take the limit as h approaches zero. To do so, set h=0.



Hence, the derivative of the given function with respect to t is `f'(t)=5/(t+3)^2` .

pramodpandey | Student















` f'(t)=5/(t+3)^2`


oldnick | Student

ya mean  `lim_(h->0) (f(a+h)-f(a))/h`