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 $u$ :

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

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