Question

If s=t/2t+1 then find ds/dt​

Answer 1

Explanation:

S = t/(2t+1)

ds/dt =

suppose : 2t+1 = a

da/dt = 2

t = a-1/2

then

S = (a-1/2)/(a)

S = (a-1)/2a

S = 1/2 - 1/2a

ds/da = +1/2a^2

ds/dt = 1/a^2 = 1/(2t+1)^2

Answer 2

Explanation:

It is given that,

$s=\dfrac{t}{(2t+1)}$............(1)

We need to differentiate equation (1) wrt t i.e. $\dfrac{ds}{dt}$

$s'=\dfrac{ds}{dt}$

$s'=\dfrac{d(\dfrac{t}{(2t+1)})}{dt}$

The differentiation can be done using quotient rule as:

$(\dfrac{f}{g})'=\dfrac{f'.g-g'.f}{g^2}$

So, on differentiating equation (1) we get:

$\dfrac{ds}{dt}=\dfrac{1}{(2t+1)^2}$

Hence, this is the required solution.