1. ## derivatives

Use the definition of the derivative to find f '(x) and f ''(x).

how do i do these?

2. Originally Posted by kyleu03
Use the definition of the derivative to find f '(x) and f ''(x).

how do i do these?
Do you know the definition of a derative? If not this is it

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

as h approaches 0 (didnt know the latex for it)

simply plug in x+h for the input for your f(x) function in the part that has (f(x)+h) and simply same with the next which is just the function you were given, now simplify and take/find the limit as it approaches 0 and repeat the process again to get the second derivative

for the first derivative's setup youll have something like

$\lim \frac{(\frac{4}{x+h})-(\frac{4}{x})}{h}$

3. yes i do but i got it wrong and i never heard of f ''(x). ???

4. Originally Posted by kyleu03
yes i do but i got it wrong and i never heard of f ''(x). ???

f''(x) is the derivative of f'(x).

5. Originally Posted by kyleu03
yes i do but i got it wrong and i never heard of f ''(x). ???
What was your answer, and show your work f'(x) which is the first derivative, and f''(x) means second derivative which means just take the derivative for the first derivative you just derived obviously

also dy/dx also means first derivative and dy^2/dx means second as well

Hint: simplify top numerator which is in fractions then you'll be dividing a fraction by a fraction which is just like taking the reciprocal of the denominator times the numerator

6. Originally Posted by kyleu03
Use the definition of the derivative to find f '(x) and f ''(x).

how do i do these?
The simplest way to do this is to write $f(x)= 4x^{-1}$ and use the "power rule".