Question

Find the derivative of f(x) = -11/x at x = 9.

Answer 1

@satellite73

Answer 2

\[f \left( x \right)=-\frac{ 11 }{ x }=-11 x ^{-1}\]
\[f \prime \left( x \right)=-11\left( -1 \right)x ^{-2}=\frac{ 11 }{ x^2 }\]
put x=9

Answer 3

\[\frac{ d }{ dx }(\frac{ -11 }{ x })= -11\times \frac{ d }{ dx }(\frac{ 1 }{ x })\]

So if oyu have th derivative of 1/x then you can get the value at x=9 from the above

Answer 4

@surjithayer so 11/81?

Answer 5

correct.

Answer 6

what is that, that you did? In my lesson i have this thing called the difference quotient, but its pretty confusing.

Answer 7

@surjithayer it looks like this:

(limh->0) ((f(x-h))-f(x))/h

Answer 8

Also thank you @surjithayer and @MrNood

Answer 9

finding a limit is called from the definition.
if you use quotient method
\[\frac{ d }{ dx }\left( \frac{ u }{ v } \right)=\frac{ v u \prime-u v \prime }{ v^2 }\]

Answer 10

when I was looking up how to work derivatives I saw that little symbol sometimes, but it wasnt in my lesson. What is it?

Answer 11

\[u \prime=\frac{ du }{ dx },v \prime=\frac{ dv }{ dx },f \prime \left( x \right)=\frac{ d }{ dx }\left\{ f \left( x \right) \right\}\]