# Thread: first principle derivative question

1. ## first principle derivative question

find the derivative of $\displaystyle \frac{4}{x+1}$ using first principles

$\displaystyle \frac {f(x+h)-f(x)}{h} = \frac {4}{(x+h)+1} - \frac{4}{x+1} * \frac{1}{h}$

this is as far as i can get i know to find a common demon i just can't get the right answer

2. Originally Posted by euclid2
find the derivative of $\displaystyle \frac{4}{x+1}$ using first principles

$\displaystyle \frac {f(x+h)-f(x)}{h} = \frac {4}{(x+h)+1} - \frac{4}{x+1} * \frac{1}{h}$

this is as far as i can get i know to find a common demon i just can't get the right answer
$\displaystyle \displaystyle\huge\ f(x+h)-f(x)=\frac{4}{x+1+h}-\frac{4}{x+1}=\left(\frac{x+1}{x+1}\right)\frac{4} {x+h+1}-\left(\frac{x+h+1}{x+h+1}\right)\frac{4}{x+1}$

$\displaystyle \displaystyle\huge=\frac{4(x+1)-4(x+h+1)}{(x+1)(x+h+1)}=-4\frac{h}{(x+1)(x+h+1)}$

Now it's convenient to divide by "h" so next find

$\displaystyle \displaystyle\huge\frac{f(x+h)-f(x)}{h}$

Then take the limit by setting "h" to zero.