Question

If $y=\frac{1}{1+x+x^{2}}$, then $\frac{dy}{dx}$ is equal to

• A. $y^2(1 + 2x)$
• B. $\frac{-\left(1+2x\right)}{y^{2}}$
• C. $\frac{(1+2x)}{2}$
• D. $-y( 1 + 2x)$
• E. $- y^2 ( 1+ 2x )$

Answer 1

Answer: (E)

Given, $y=\frac{1}{1+x+x^{2}} $
$\Rightarrow \, 1+x+x^{2}=\frac{1}{y}$
On differentiating w.r.t. $x$, we get
$ 0+1+2 x=-\frac{1}{y^{2}}\, \frac{d y}{d x}$
$\Rightarrow \, \frac{d y}{d x} =-(1+2 x) y^{2}$