Question

Find
f '(x).
f(x) = x2 + 6x + 9/x. I'm stuck in particular at taking the derivative of 9/x.
I have 2x+6-9/x^10.. What am I doing wrong?

Answer 1

Is that all over x or just the 9?

Answer 2

the derivative of 9/x
is the same as 9 times the derivative of 1/x

1/x is the same as x^-1

the derivative of x^n is nx^{n-1}

Answer 3

If it is just the 9 that is over the x, then f'(x) = 2x + 6 -9/x^2, since the 9/x could be looked at as 9x^(-1), so the derivative of that would be -9x^(-2)

Answer 4

it is just that the 9/x

Answer 5

Ok, then what UnkleRhaukus and I said would apply. :)

Answer 6

so is the exponent + or -?

Answer 7

The exponent is -.

Answer 8

k, thanks :)

Answer 9

since you started with 9/x or 9x^(-1)

Answer 10

So then using the power rule, the derivative would be -1(9x^(-2)) or -9x^(-2) or -9/x^2

Answer 11

So you can use the negative exponent, or if you want to use a positive exponent you can use the equivalent expression -9/x^2. Whichever you prefer. :)

Answer 12

ok, I think I got it now. I'm sure I'll have more derivative questions on the way :)

Answer 13

Ok :D