Question

Find the derivative of f(x) = 6/x at x = -2.

Answer 1

-3/2

Answer 2

Can you explain how you got that cuz i wanna be able to do the other problems i have

Answer 3

Do you just substitute?

Answer 4

differentiate then substitute

Answer 5

differentiate?

Answer 6

yes, derivative means u have to differentiate

Answer 7

How do you differentiate?

Answer 8

f(x) = 6 x^(-1)

df/dx = (-1)* 6 *X^(-2)

Answer 9

now substitute x= -2

Answer 10

which is give -3/2

Answer 11

sorry to keep saying thisbut i'm still confused. as tohow you got this "df/dx = (-1)* 6 *X^(-2)"

Answer 12

f(x) = 6 * x^(-1)

Answer 13

now if u do the differentiation

Answer 14

Use the power rule to differentiate... multiply by the power, and reduce the power by one, or: \[\Large \frac{ d }{ dx } x^n = n x ^{n-1}\]
\[ \Large f(x) =\frac{ 6 }{ x} = 6x^{-1}\]
So multiply by the power (-1) and reduce the power by one (-1 -1 = -2):\[\Large \frac{ d }{ dx} (6x^{-1}) = -1*6 x^{-2}\]

Answer 15

Following @agent0smith, for this problem, n = 1 and x is in the denominator:
\[6*\frac{ d}{ dx } (1/x^{n}) = 6\frac{ d}{ dx } x^{-n} = -n *6 x^{-n -1}=6\frac{-n}{x^{n+1}}\]

Answer 16

Thank you^^