Could use some Derivation help, please

Okay so I just started with derivation.. it's pretty damn fun but the Swedish standard math book sucks completly because they can't give a decent example even if their life depended on it.

Anywho here is problem.

Calculate f`(4) by using numeric derivation, if;

a) f(x) = 3x^4 -350x + 129

b) f(x) = x / (x^2 + 1)

c) f(x) = 6.5 * 10^(0,0086x)

On a) I tried to use the basic lim h > 0, it did work but there was so many damn numbers It's like made for you to screw up.

f(4+h) - f(4)

3(4+h)^4 - 350(4+h) + 129

You see it right? (4+h)^4 is pure pain to keep track of.. is there an easier way for me to simplify this so the calculation won't get so long?

On b) I got stuck completly.

f(4+h) -f(4) = ((4+h) / ((4+h)^2 +1))) - 4 / (4^2 + 1)

Could someone help me expand this and give me some derivation tips?

P.S Thx to your help I got a B+ on my last math thest which I've never had before! Thanks ALOT!

D.S

I'll let moo take the work

Quote:

Originally Posted by

**Hanga** Yeah I know the

$\displaystyle \text{What \ is \ } \lim_{h \to 0} \frac{f(4+h)-f(4)}{h}$

I do not know this one

$\displaystyle f'(a)=\lim_{x \to a} \frac{f(x)-f(a)}{x-a}$ ?

Simply because there is no example on how to execute this in my lousy **** book...

enlighten me S.V.P :)

I tired using this;

(f(4+h) - f(4) / h)[/quote]

but the second one is the alternate form of the deriavative that says f'(x) evaluated at c is $\displaystyle f'(c)=\lim_{x \to c}\frac{f(x)-f(c)}{x-c}$