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.
Hi buddy.
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
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.
I am sure you have seen the rule before.
Wikipedia says: Sum rule in differentiation - Wikipedia, the free encyclopedia
Best regards,
Rapha