найти производную: у=ln корень (3х-4)/(3х+1)

Ответ:

y(x) = ln(3x+1)

\begin{gathered}y' = \frac{1}{3x+1} * 3 = \frac{3}{3x+1} \ \textgreater \ 0 \\ \frac{3}{3x+1} \ \textgreater \ 0 \\ x = -\frac{1}{3} \\ -----( -\frac{1}{3}) ++++\ \textgreater \ \\ x \in (-\frac{1}{3}; +\infty)\end{gathered}

y

′

=

3x+1

1

∗3=

3x+1

3

\textgreater 0

3x+1

3

\textgreater 0

x=−

3

1

−−−−−(−

3

1

)++++ \textgreater

x∈(−

3

1

;+∞)