answer to this problem?

Question

use the definition of the derivative to compute the derivative of f(x)= (x+1)/(x-4)

its only asking me to find the derivative of the function right?
and the answer is (-5x)/(x-4)^2 right?

i just want to know cause i got this wrong on the test

Answer 1

The derivative is [(x-4)- (x+1)]/(x-4)^2 = -5/(x-4)^2

If we use the definition of the derivative:


dy/dx = Lim h -> 0 {f(x+h) -f(x)}/h
= lim h-> 0 [(x+h+1)/(x+h-4) - (x+1)/(x-4)]/h
(x+h+1)(x-4)-(x+1)(x+h-4)
= lim x-> 0 ---------------------------------------
(x+h-4)(x-4)h

= lim h-> 0 -5h/(x+h-4)(x-4)h = -5/(x-4)^2

Answer 2

i'm getting just -5/(x-4)^2
is that what you meant?
if so, mabye you didn't use the definition of derivative (the limit usage)

Answer 3

the ans is 5 / ( x-4)^2

Answer 4

a=(x+1) b=(x-4)

a'b-ab'/b^2