Question

The derivative of $\frac{2}{(x+1)}$ with respect to x will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

As we can see that the given function is the quotient of two functions:
Numerator is 2
Denominator is x + 1
So we can apply the quotient rule
$\frac{d}{dx}\left(\frac{f\left(x\right)}{g\left(x\right)}\right)=\frac{\left(f^{\prime }\right(x\left)g\right(x\left)\right)-g^{\prime }\left(x\right)f\left(x\right)}{\left(g\right(x){)}^2}$

$f\left(x\right)=2,f^{\prime }\left(x\right)=0$
$\left(g\right(x)=(x+1),g^{\prime }(x)=1$

So $\frac{d}{dx}\left(\frac{2}{x+1}\right)=\frac{0(x+1)-2\times 1}{(x+1{)}^2}=\frac{-2}{(x+1{)}^2}$