What is the derivative of #F(x) = 1/(x-5)#?

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Answer 1 · 2015-06-07T15:23:37

We can use the chain rule here, renaming #u=x-5#.

The chain rule states that #(dy)/(dx)=(dy)/(du)(du)/(dx)#

Also, one law of exponentials states that #1/a^n=a^-n#.

Thus, our new function becomes #u^-1#.

Derivating...

#(dy)/(dx)=-u^-2*(1)#

Substituting #u#:

#(dy)/(dx)=-(x-5)^-2=-1/(x-5)^2#