Question

Find the derivative of f(x)=5-|x-5|

Answer 1

this is d/dx (5) - d/dx (x-5)

derivative of 5 = 0..and the derivative of x-5 = 1

so..

0-1 = -1

Answer 2

wouldnt you have a +/- value since its absolute value?

Answer 3

As there is a absolute value, we have to consider two cases.
f(x)=5-|x-5|
case i), for x>5
f(x) = 5-(x-5)
= 5-x+5
=10-x
f'(x) =-1
case ii) for x<=5,
f(x)= 5-(-(x-5) )
=5+(x-5)
=x
f'(x)=1

Answer 4

oh wait..that was absolute value?? so sorry! thought they were parentheses

Answer 5

my eyes are failing baaad

Answer 6

If the problem is 1/(x - 5), then, by the power rule, the derivative is:

-1/(x - 5)^2

The slope, m, of the tangent line is the derivative evaluated at the x-coordinate of the point. Plug in -4 for x:

m = -1/(-4 - 5)^2 = -1/81

Then solving y = mx + b for the y-intercept after plugging in the point:

-1/9 = 4/81 + b

b = -1/9 - 4/81 = -13/81

Tangent line equation is:

y = -1/81*x - 13/81

Hope this helps.

Answer 7

1/(x-5) = (x-5)^-1. Then you use the chain rule to take the derivative.

Answer 8

you can treat it as a piece-wise function. so if you want the derivative, f'(x) will be something different depending on the x you look at...