1. ## the derivative

Find a formula for the derivative of the function algebraically.

n(x) = (4/x) +9

n(x) = ?

i tried this one using the rate of change formula, and i got 1/x and i got it wrong so if you tell me what i did wrong and how to fix it. any help would be great, thank you.

2. Originally Posted by mer1988
Find a formula for the derivative of the function algebraically.

n(x) = (4/x) +9

n(x) = ?

i tried this one using the rate of change formula, and i got 1/x and i got it wrong so if you tell me what i did wrong and how to fix it. any help would be great, thank you.
the derivative is the "instantaneous rate of change," so using the regular rate of change formula will not give you the correct answer. if you want to go from first principles, you must use:

$f'(x) = \lim_{h \to 0} \frac {f(x + h) - f(x)}h$

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

if you don't have to go by first principles, note that $n(x) = \frac 4x + 9 = 4x^{-1} + 9$

you can use the power rule on the right hand side