hey everyone

havin a bit of trouble with this,

f(3) = -2
f'(3) = 5

find g'(3) if

a. g(x) = 3x^2 - 5f(x)

b. g(x) = (3x + 1) / f(x)

i've tried differentiating it and subbing it in but no luck, thanks in advance.

2. Hi buddy.

Originally Posted by jimzer
hey everyone

havin a bit of trouble with this,

f(3) = -2
f'(3) = 5

find g'(3) if

a. g(x) = 3x^2 - 5f(x)

b. g(x) = (3x + 1) / f(x)

i've tried differentiating it and subbing it in but no luck, thanks in advance.
do you know this rule:

g(x) = f(x) + h(x)+...

=> g'(x) = f'(x) + g'(x)+...

Therefor

a) $\displaystyle g(x) = 3x^2 - 5f(x)$

=> $\displaystyle g'(x) = (3x^2)' - 5 f'(x)$

$\displaystyle g'(x) = 6x - 5f'(x)$

$\displaystyle g'(3) = 6*3 - 5*f'(3)$

done

b) Use the quotient rule, then you get

$\displaystyle g'(x) = \frac{(3x+1)' * f(x) - f'(x)*(3x+1)}{[f(x)]^2}$

$\displaystyle = \frac{3*f(x) - f'(x) (3x+1)}{[f(x)]^2}$

Now x = 3

....

Guess you can do it yourself, can't you?

Yours,
Rapha

3. thanks a lot man, i've never been taught the g(x) = f(x) + h(x) rule before...

if its not too much trouble can you explain to me what it is?

you've been a huge help!! thanks and rep given!!

4. Originally Posted by jimzer
thanks a lot man, i've never been taught the g(x) = f(x) + h(x) rule before...

if its not too much trouble can you explain to me what it is?

When you have a function, say g(x), that equals other functions added together

g(x) = f(x) + h(x) + m(x) + j(x) ...

then

g'(x) = f'(x) + h'(x) + m'(x) + j'(x) ...

This is from the addition rule of differentiation. There are other rules for multiplication, division, and multiplication by a constant. Here is a brief list of them: rules

Hope that is what you meant.

5. Originally Posted by jimzer
thanks a lot man, i've never been taught the g(x) = f(x) + h(x) rule before...

if its not too much trouble can you explain to me what it is?
I am sure you have seen the rule before.

Wikipedia says: Sum rule in differentiation - Wikipedia, the free encyclopedia

Best regards,
Rapha