HELP ASAP <br> stats and probs

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

wlad13 [49]

Answer:

$\frac{dy}{dx}=\frac{x(1-2lnx)}{x^{4}}$

Step-by-step explanation:

To solve the question we refresh our knowledge of the quotient rule.

For a function f(x) express as a ratio of another functions u(x) and v(x) i.e

$f(x)=\frac{u(x)}{v(x)}\\$ , the derivative is express as

$\frac{df(x)}{dx}=\frac{v(x)\frac{du(x)}{dx}-u(x)\frac{dv(x)}{dx}}{v(x)^{2} }$

from $y=lnx/x^{2}$

we assign u(x)=lnx and v(x)=x^2

and the derivatives

$\frac{du(x)}{dx}=\frac{1}{x}\\\frac{dv(x)}{dx}=2x\\$ .

Note the expression used in determining the derivative of the logarithm function.it was obtain from the general expression of logarithm derivative i.e $y=lnx\\\frac{dy}{dx}=\frac{1}{x}$

If we substitute values into the quotient expression we arrive at

$\frac{dy}{dx}=\frac{(x^{2}*\frac{1}{x})-(2x*lnx)}{x^{4}}\\\frac{dy}{dx}=\frac{x-2xlnx}{x^{4}}\\\frac{dy}{dx}=\frac{x(1-2lnx)}{x^{4}}$

8 0

3 years ago

ky has 3 times more books than grant and grant has 6 fewer books than Jaime if the total combined number of books is 176 how man

sergiy2304 [10]

Number of books each of them have:

Jaime: x
Grant: x - 6
Ky: 3 (x - 6)

There are 176 books in total, so we can write it down as:

176 = x + x - 6 + 3 (x - 6)
176 = x + x - 6 + 3 * x + 3 * (-6)
176 = x + x - 6 + 3x - 18
176 = 2x - 6 + 3x - 18
176 = 5x - 24 / + 24 (both sides)
5x = 200 / ÷ 5 (both sides)
x = 40

Doublecheck:

Jamie: 40
Grant: 40 - 6 = 34
Ky: 3 (40 - 6) = 3 * 34 = 102

102 + 34 + 40 = 176, so it's correct :)

5 0

3 years ago

Read 2 more answers

Which of these statements best describes the relation shown in Item 1?

Misha Larkins [42]

Answer:

It is a many-to-one relation

Step-by-step explanation:

Given

See attachment for relation

Required

What type of function is it?

The relation can be represented as:

$\left[\begin{array}{c}x\\ \\-5\\-2\\1\\5\end{array}\right]$ $\left[\begin{array}{c}y\\ \\10\\11\\4\\10\end{array}\right]$

Where

$x = domain$ and $y = range$

Notice that the range has an occurrence of 10 (twice)

i.e.

$(x_1,y_1) = (-5,10)$ and $(x_2,y_2) = (5,10)$

In function and relations, when two different values in the domain point to the same value in the range implies that, <em>the relation is many to one.</em>