# Thread: Limit definition and derivative

1. ## Limit definition and derivative

If I have to use the limit definition to find the derivative and I have a f(x)= 1/square root(x+a number)....how would I start this off? Do I just leave it the same or do I have to change it? Thanks

2. Originally Posted by Minnesota1
If I have to use the limit definition to find the derivative and I have a f(x)= 1/square root(x+a number)....how would I start this off? Do I just leave it the same or do I have to change it? Thanks
Step 1:multiply by :

.......... $\frac{\sqrt{x+a}}{\sqrt{x+a}}$ to get:

............... $\frac{\sqrt{x+a}}{x+a}$..............................

Step 2: form the ratio: $\frac{f(x+h)-f(x)}{h}$ to get,after doing some calculations:

................... $\frac{(x+a)\sqrt{x+h+a}-(x+h+a)\sqrt{x+a}}{h(x+a)(x+h+a)}$.................................................. ......................

Step 3: multiply by:

.............. $\frac{(x+a)\sqrt{x+h+a}+(x+h+a)\sqrt{x+a}}{(x+a)\s qrt{x+h+a}+(x+h+a)\sqrt{x+a}}$ to get after doing some calculations:

.....................- $\frac{ 1}{(x+a)\sqrt{x+h+a}+(x+h+a)\sqrt{x+a}}$.................................................. ...................

Step 4: let h go to zero to get:

...................-1/2 $\frac{ 1}{(x+a)\sqrt{x+a}}$ ,which is the desired limit............................................. .....................................