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2 years ago

Find the derivative g(x)=ln(2x^2+1)

Mathematics

1 answer:

lana [24]2 years ago

8 0

Answer:

4x / (2x^2+1)

Step-by-step explanation:

g(x)=ln(2x^2+1)

Using u substitution

u= 2x^2 +1

du = 4x dx

g'(x) = d/du ( g(u) du)

We know that the derivative of ln(u) = 1/u since this is always positive

= 1/ u* du

Substituting x back into the equation

g'(x) = 1/(2x^2+1) * 4x

= 4x / (2x^2+1)

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The plot below shows the graphs of three functions, f, g, and h, all of which determine the population of three different cities

monitta

So, here we have an exponential function.

Remember that an exponential function has the form:

$y=a(b)^x=a(1\pm\frac{r}{100})^x$

Where a represents an initial amount, and r is the rate of this amount to change. (Increase, or decrease).

So, given that the population of City A in 2000 was 40 thousand people and the population increased by 13% each year, we can say that

$\begin{gathered} a=40 \\ b=1+\frac{13}{100}=1.13 \end{gathered}$

So,

$f(x)=40(1.13)^x$

For city B:

$\begin{gathered} a=40 \\ b=1+\frac{16}{100}=1.16 \\ g(x)=40(1.16)^x \end{gathered}$

But something different happens with city C. This is not an exponential function, this is a linear function.

So,

$h(x)=40+10x$

7 0

10 months ago

Find the product 4 2/3 x 3 3/4

storchak [24]

Answer:

45.6

Step-by-step explanation:

trust me bro(don't)

7 0

2 years ago

Read 2 more answers

ANSWER AS MANY THROUGH 1 and 9 FOR 15 POINTS

Tamiku [17]

Number 9 is 1.52 because you divide 15.3 by 10 it will be 1 .52

7 0

3 years ago

2x + 1 = 9<br> is that the answer ?

Ronch [10]

Answer:

yes

Step-by-step explanation:

because 9-1=8/2 equals 4 so2x4+1=9

7 0

2 years ago

7. f(x)=2+x+1<br> What is the domain

Fed [463]

Answer:

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

7 0

3 years ago

Read 2 more answers