Finding the Derivative of f(a) with Definition

[Al3x L3g3nd]

Homework Statement

Find derivative of f(a) for f(t)=(2t+1)/(t+3) using the definition of a derivative

Homework Equations

f '(a)=lim as x goes to a of (f(x)-f(a))/(x-a)

The Attempt at a Solution

f '(a)=lim as x goes to a of (f(x)-f(a))/(x-a)
f '(a)=lim as t goes to a of (((2t+1)/(t+3))-((2a+1)/(a+3)))/(t-a)
f '(a)=lim as t goes to a of (((2t+1)(a+3))/((t+3)(a+3)))-(((2a+1)(t+3))/((a+3)(t+3)))
simplified and got
f '(a)=lim as t goes to a of ((-5a+5t)/((a+3)(t+3)))/(t-a)

I don't know where to go from here.

 

[LCKurtz]

Homework Statement

Find derivative of f(a) for f(t)=(2t+1)/(t+3) using the definition of a derivative

Homework Equations

f '(a)=lim as x goes to a of (f(x)-f(a))/(x-a)

The Attempt at a Solution

f '(a)=lim as x goes to a of (f(x)-f(a))/(x-a)
f '(a)=lim as t goes to a of (((2t+1)/(t+3))-((2a+1)/(a+3)))/(t-a)
f '(a)=lim as t goes to a of (((2t+1)(a+3))/((t+3)(a+3)))-(((2a+1)(t+3))/((a+3)(t+3)))
simplified and got
f '(a)=lim as t goes to a of ((-5a+5t)/((a+3)(t+3)))/(t-a)

I don't know where to go from here.

Rewriting your last equation in readable form:$$
\frac{-5a+5t}{(a+3)(t+3)(t-a)}$$You are almost there. Factor a 5 out of the numerator, cancel like factors, and let $t\to a$ and you will have it.

 

[Al3x L3g3nd]

Rewriting your last equation in readable form:$$
\frac{-5a+5t}{(a+3)(t+3)(t-a)}$$You are almost there. Factor a 5 out of the numerator, cancel like factors, and let $t\to a$ and you will have it.

wow i feel dumb for not realizing that.

thanks :)