Find the derivative of f(x) = 7x + 9 at x = 6.

Question

hartnn · Answer

do you know how to find derivatives ?

derivative of x^n is ?

anonymous · Answer

I do not remember @hartnn

precal · Answer

use the power rule

anonymous · Answer

Which is

hartnn · Answer

$\Large \dfrac{d}{dx} x^n = n x^{n-1}$

hartnn · Answer

for$ 7x =7x^1 $

the exponent is 1, so plug in n=1

anonymous · Answer

so that would be 7

hartnn · Answer

yes,
and derivative of constant = 0

so derivative of  7x + 9 is simply 7

anonymous · Answer

Okay so for 4/x and x=2, would it be 4?

hartnn · Answer

nopes,

4/x is $\Large 4 x^{-1}$
so you will have to plug in x= -1 in that formula

anonymous · Answer

-4?

hartnn · Answer

no, what did you get after plugging in n =-1 in that formula ?

$\Large (-1)x^{-1-1} = ... ?$

anonymous · Answer

wait plug in -1 for x in 4/x? 4/-1

hartnn · Answer

no, plug in -1 for n in the formula for derivative

anonymous · Answer

Haha I'm confused now, sorry

hartnn · Answer

you want derivative of $x^{-1}$
and you have the formula as
$\Large \dfrac{d}{dx} x^n = n x^{n-1}$

hartnn · Answer

so naturally, you will select n as -1

hartnn · Answer

$\Large \dfrac{d}{dx} x^{-1} = (-1)x^{-1-1} =...?$

anonymous · Answer

0?

hartnn · Answer

no..
what is -1-1 = .. ?

anonymous · Answer

-2 lol sorry

hartnn · Answer

yeah,
so 
derivative of x^-1 = -1 x^-2

derivative of 4 x^-1 will be -4 x^-2 = -4/x^2 
now you can plug in x=2 here

anonymous · Answer

-2

anonymous · Answer

wait i  read that wrong

anonymous · Answer

-1

hartnn · Answer

-4/2^2 = -4/4 = -1
yes! you're correct :)

anonymous · Answer

Thank you (:

hartnn · Answer

welcome ^_^