Mathematics: Use logarithmic differentiation to find the derivative of y with respect to the given independent variable. y equals (t )(t plus 2 )(t plus 6 ).

Use logarithmic differentiation to find the derivative

Ответ:

vanessa5325

21.01.2022

Mathematics

$y' = [t^{(t+2)\cdot (t + 6)}]\cdot \left[(2\cdot t + 8)\cdot \ln t + \frac{t^{2}+8\cdot t + 12}{t} \right]$

Step-by-step explanation:

The function is:

$y = t^{(t+2)\cdot (t+6)}$

By using natural logarithmics and algebraic handling on both sides:

$\ln y = (t+2)\cdot (t+ 6)\cdot \ln t$

$\ln y = (t^{2}+8\cdot t + 12)\cdot \ln t$

The logarithmic differentiation is:

$\frac{1}{y}\cdot y' = (2\cdot t + 8)\cdot \ln t + \frac{t^{2}+8\cdot t + 12}{t}$

$y' = y\cdot \left[(2\cdot t + 8)\cdot \ln t + \frac{t^{2}+8\cdot t + 12}{t} \right]$

$y' = [t^{(t+2)\cdot (t + 6)}]\cdot \left[(2\cdot t + 8)\cdot \ln t + \frac{t^{2}+8\cdot t + 12}{t} \right]$

0,0(0 оценок)

Ответ:

greennakareya

22.01.2023

Mathematics

The description of the given scenario is explained below.

Step-by-step explanation:

Mathematics language may be mastered, although demands or needs the requisite attempts to understand every language other than English. The mathematics makes it so much easier for mathematicians to convey the kinds of opinions they want. It is as follows:

Precise: capable of making very fine marks. Concise: capable of doing something very briefly. Powerful: capable of voicing intelligent concepts with minimal effort.

0,0(0 оценок)

Use logarithmic differentiation to find the derivative of y with respect to the given independent variable. y equals (t )(t plus 2 )(t plus 6 ).

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question