00:01
In this question, we are asked to find the derivative of the function f using the definition of the derivative.
00:05
And by the definition, f prime of x equals to the limit as h goes to 0 of f of x plus h minus f of x divided by h.
00:24
So there are a few things we need to do before we can calculate this limit.
00:32
First of all, we need to figure out what is f of x plus h.
00:39
To get f of x plus h, we simply need to replace x in the expression for f of x by x plus h.
00:47
And we are going to get 1 over 10 multiplied by x plus h minus 1 over 8.
00:58
And this equals to 1 over 10 x plus 1 over 10 h minus 1 over 8.
01:10
Now we are ready to calculate f prime of it.
01:13
F prime of h.
01:14
F prime of x.
01:15
F prime of x equals to the limit as h goes to zero now we are going to replace f of x plus h by its expression 1 over 10 x plus 1 over 10 h minus 1 over 8 minus f of x which equals to 1 over 10 x minus 1 over 8 all right let me make my writing more compact so that we can fit in one in one line so we are going to get the limit as h goes to 0.
02:05
1 over 10x plus 1 over 10 h minus 1 over 8 minus 1 over 10 x minus 1 over 8.
02:25
Alright, this is better...
