Check the solution to "Find the indicated derivatives. dsdtifs=t2t+1" - Plainmath

a2linetagadaW

Answered question

2021-04-20

Find the indicated derivatives.

\frac{d s}{d t} if s = \frac{t}{2 t + 1}

Answer & Explanation

Liyana Mansell

Skilled2021-04-22Added 97 answers

Step 1
The given function is

s = \frac{t}{2 t + 1}

Step 2
Find the derivative

\frac{d s}{d t}

\frac{d s}{d t} = \frac{d}{d t} (\frac{t}{2 t + 1})

= \frac{(2 t + 1) \frac{d}{d t} (t) - t \frac{d}{d t} (2 t + 1)}{{(2 t + 1)}^{2}}

= \frac{(2 t + 1) (1) - t (2)}{{(2 t + 1)}^{2}}

= \frac{2 t + 1 - 2 t}{{(2 t + 1)}^{2}}

= \frac{1}{{(2 t + 1)}^{2}}

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