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3 years ago

Dy/dx of ln(x/x^²+1)

1 answer:

5 0

$\dfrac{dy}{dx}\ \ln\left(\dfrac{x}{x^2+1}\right)=\dfrac{1}{\frac{x}{x^2+1}}\cdot\dfrac{x'(x^2+1)-x(x^2+1)'}{(x^2+1)^2}\\\\=\dfrac{x^2+1}{x}\cdot\dfrac{1(x^2+1)-x(2x)}{(x^2+1)^2}=\dfrac{1}{x}\cdot\dfrac{x^2+1-2x^2}{x^2+1}=\dfrac{1-x^2}{x^3+x}\\\\Used:\\\\(\ln(x))'=\dfrac{1}{x}\\\\\left[f(g(x))\right]'=f'(g(x))\cdot g'(x)\\\\\left(\dfrac{f(x)}{g(x)}\right)'=\dfrac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}$

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Distributing, formulas, and addition

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3 years ago

Domain and range and function , need ASAP

Diano4ka-milaya [45]

Answer:

Domain: $-2\leq x\leq 2$

Range: $0\leq y\leq 4$

Step-by-step explanation:

The domain of a function is the set of values that one can input into a function and get a valid result.

The range of a function is the set of valid outputs that one can attain when a value is substituted into a function.

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3 years ago

Marty is taking piano lessons. She is going to practice every afternoon. The 1st week she practiced for 11 minutes each day. The

defon

Answer:

$m=7w+4$

Step-by-step explanation:

<u>Linear Modeling</u>

It consist is setting up a linear relationship between two variables, given some experimental data. Only 2 points are needed to set up the equation of a line, but if more than 2 points are used, then the result should use statistical approaches like linear regression to find the best-fit line.

For the question at hand, Marty practices his piano lessons 11 minutes the week #1. It provides the first point (1,11). He practices 25 minutes per day on the third week. It gives us another point (3,25). This is enough to find the equation of a line. The general formula for a line, having two points (m1,w1) (m2,w2) is

$\displaystyle m-m_1=\frac{m_2-m_1}{w_2-w_1}(w-w_1)$

Let's plug in our values

$\displaystyle m-11=\frac{25-11}{3-1}(w-1)$

Simplifying:

$m-11=7w-7$

$\boxed{m=7w+4}$

3 0

3 years ago

Lisa paid 43.95 for 16.1 gallons of gasoline.What was the cost per gallon,rounded to the nearest hundredth?Show your work

GrogVix [38]

Cost per gallon is found by dividing the cost by the number of gallons.

$43.95/16.1 ≈ $2.7298137

Rounded to hundredths, this is $2.73.

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3 years ago

Debbie has $460 in a savings account that earns 8% annually. If the interest is not compounded, how much interest will she earn

Bess [88]

She earned $184 in interest
$644 In all

Here's why:
The formula is Interest = Principal x Rate x Time
I = 460 x 8% x 5 or I = 460 x 0.08 x 5. PEMDAS
460(0.08) = 36.8
I = 36.8 x 5
36.8 x 5 = 184
I = $184
To find them in all, add the original amount she deposited with the interest.
460 + 184 = 644
In all: $644

6 0

3 years ago

Read 2 more answers