Question

find the derivative by definition
y=1/x

Answer 1

-1/x^2

Answer 2

derivative (x)^-1
is
-1 x^-2

you can rewrite
-1/x^2

Answer 3

by definition, do you mean taking the limit of the difference quotient?

Answer 4

yeah by definiton means taking limit

Answer 5

\[\lim_{h\to 0} \, \frac{\frac{1}{h+x}-\frac{1}{x}}{h}\]

Answer 6

\[\lim_{h\to 0} \, \frac{-\frac{h}{x (h+x)}}{h}\]

Answer 7

\[\lim_{h\to 0} \, {-\frac{h}{x h(h+x)}}\]
\[\lim_{1\to 0} \, {-\frac{1}{x (h+x)}}\]

Answer 8

as h goes to 0 , -1/x^2

Answer 9

can you please solve it with y+lemda y rule

Answer 10

I am not sure what you mean?