Question

differentiate [1/2x+1]​

Answer 1

Answer:

$\frac{dy}{dx}=\frac{-2}{4x^2+4x+1}$

Explanation:

$y = \frac{1}{2x+1}$

To find the derivative of the given expression:

Differentiating  w.r.t $x$

using chain rule:

⇒ $\frac{dy}{dx}=$ $-\frac{1}{\left(2x+1\right)^2}\frac{d}{dx}\left(2x+1\right)$

⇒$\frac{dy}{dx}=$$-\frac{1}{\left(2x+1\right)^2}\cdot \:2$

On Simplifying we get,

⇒$\frac{dy}{dx}=\frac{-2}{4x^2+4x+1}$  (Ans.)