How do you find the derivative of $2/(x+1)$ ?

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Answer 1 · 2015-06-01T19:47:50

This expression can be rewritten as $2(x+1)^-1$ , following the exponential alw that states $a^-n=1/a^n$ .

Naming $u=x+1$ , we can rewrite the expression as $y=2u^-1$ and, thus, derivate it according to the chain rule, which states that

$(dy)/(dx)=(dy)/(du)(du)/(dx)$

So,

$(dy)/(du)=-2u^-2$

$(du)/(dx)=1$

Thus

$(dy)/(dx)=(-2u^-2)(1)=-2(x+1)^-2=color(green)(-2/(x+1)^2)$

How do you find the derivative of 2/(x+1)2/(x+1)?