- #1

- 97

- 0

f(x) = x/(x+c/x)

through simplication, i got:

x(x+cx^-1)^-1

=x(x^-1 + c^-1*x)

=1+1/c*x^2

taking the derivative,

-c^-2*x^2 + c^-1*2x

its wrong though so where did i go wrong?

- Thread starter nothing123
- Start date

- #1

- 97

- 0

f(x) = x/(x+c/x)

through simplication, i got:

x(x+cx^-1)^-1

=x(x^-1 + c^-1*x)

=1+1/c*x^2

taking the derivative,

-c^-2*x^2 + c^-1*2x

its wrong though so where did i go wrong?

- #2

- 2,063

- 2

That's not right. (x+y)nothing123 said:through simplication, i got:

x(x+cx^-1)^-1

=x(x^-1 + c^-1*x)

=1+1/c*x^2

Without simplifying the original expression you could have used the quotient rule to find the derivative, OR you could differentiate x(x+cx^-1)^-1 using the product rule.

- #3

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 956

[tex]f(x)= \frac{x}{x+ \frac{c}{x}}= \frac{x^2}{x^2+ c}[/tex]

for all x except 0.

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