Question

Obtain the differential coefficient of 1/2x+1​

Answer 1

Step-by-step explanation:

d/dx(1/2x+1)

={(2x+1).d/dx(1) - 1.d/dx(2x+1)}/(2x+1)^2

= - 2/(2x+1)^2

Answer 2

The differential coefficient of  $\frac{1}{2x+1}$ is -2.

Step-by-step explanation:

Given : Expression $\frac{1}{2x+1}$.

To find : Obtain the differential coefficient of expression ?

Solution :

Applying division rule of differentiation,

$\frac{d}{dx}(\frac{u}{v})=\frac{vu'-uv'}{v^2}$

Here, u=1 and v=2x+1

$u'=\frac{d}{dx}(1)=0$

$v'=\frac{d}{dx}(2x+1)=2$

Substitute,

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

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

Therefore, the differential coefficient of  $\frac{1}{2x+1}$ is -2.

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