Question

How do you find the derivative of this function?

Answer 1

\[\frac{ x+1 }{ x-1 }\]

Answer 2

use the quotient rule: http://en.wikipedia.org/wiki/Quotient_rule

Answer 3

Have you learned the quotient rule?

Answer 4

Yes I have, I'll try using that.

Answer 5

Let me know what you get.

Answer 6

(x+1)/(x-1)

Find the derivative of the expression.
(d)/(dx) (x+1)/(x-1)

Use the quotient rule to find the derivative of ((x+1))/((x-1)). The quotient rule states that ((f)/(g))'=((f'g-fg'))/((g^(2))').
((d)/(dx) [(x+1)]((x-1))-((x+1))((d)/(dx) [(x-1)]))/(((x-1))^(2))

Find the derivative of the expression.
(d)/(dx) (x+1)

Remove the parentheses around the expression x+1.
x+1

To find the derivative of x, multiply the base (x) by the exponent (1), then subtract 1 from the exponent (1-1=0). Since the exponent is now 0, x is eliminated from the term.
(d)/(dx) x+1=1+(d)/(dx) 1

Since 1 does not contain x, the derivative of 1 is 0.
(d)/(dx) x+1=1+0

Add 0 to 1 to get 1.
(d)/(dx) x+1=1

Find the derivative of the expression.
(d)/(dx) (x-1)

Remove the parentheses around the expression x-1.
x-1

To find the derivative of x, multiply the base (x) by the exponent (1), then subtract 1 from the exponent (1-1=0). Since the exponent is now 0, x is eliminated from the term.
(d)/(dx) x-1=1+(d)/(dx) -1

Since -1 does not contain x, the derivative of -1 is 0.
(d)/(dx) x-1=1+0

Add 0 to 1 to get 1.
(d)/(dx) x-1=1

Substitute each function and derivative into the quotient rule formula.
(d)/(dx) (x+1)/(x-1)=((1)(x-1)-(x+1)(1))/((x-1)^(2))

Remove the factor of 1 from the expression.
(d)/(dx) (x+1)/(x-1)=(x-1)/((x-1)^(2))-((x+1)(1))/((x-1)^(2))

Reduce the expression by canceling out the common factor of (x-1) from the numerator and denominator.
(d)/(dx) (x+1)/(x-1)=(<X>(x-1)<x>)/((x-1)^(<X>2<x>))-((x+1)(1))/((x-1)^(2))

Reduce the expression by canceling out the common factor of (x-1) from the numerator and denominator.
(d)/(dx) (x+1)/(x-1)=(1)/(x-1)-((x+1)(1))/((x-1)^(2))

Multiply -1 by 1 to get -1.
(d)/(dx) (x+1)/(x-1)=(1)/(x-1)-(x+1)/((x-1)^(2))

Remove the factor of 1 from the numerator.
(1)/(x-1)-(x+1)/((x-1)^(2))