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Setler [38]
3 years ago
6

Dy/dx of ln(x/x^²+1)

Mathematics
1 answer:
exis [7]3 years ago
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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Solve for x in the following system (show work)<br><br> 3x+4y=8<br> y=3x+17
vodka [1.7K]
3x + 4(3x+17) = 8
3x + 12x + 68 = 8
15x = - 60
x = - 4

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7 0
2 years ago
A sphere-shaped water balloon can extend to a diameter of 3.5 inches before it explodes.
ollegr [7]
Volume of a spehere=(4/3)πr³

Data:
diameter=3.5 in
π=3.14

1)we calculate the radius:
r=diameter/2=3.5 in / 2=1.75 in

2) we calculate the volume of this sphere:
volume=(4/3)*3.14*(1.75 in)³=22.4379...in³≈22.44 in³.

Answer: 22.44 in³
5 0
3 years ago
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(4x+5)(x^2+2x+3) help?
Leya [2.2K]
This is the right anwser

5 0
3 years ago
Which expression is equivalent to...? Screenshots attached. Please help! Thank you.
Studentka2010 [4]

Answer:

4x^{3} y^{2} (\sqrt[3]{4 x y})

Step-by-step explanation:

Another complex expression, let's simplify it step by step...

We'll start by re-writing 256 as 4^4

\sqrt[3]{256 x^{10} y^{7} } = \sqrt[3]{4^{4} x^{10} y^{7} }

Then we'll extract the 4 from the cubic root.  We will then subtract 3 from the exponent (4) to get to a simple 4 inside, and a 4 outside.

\sqrt[3]{4^{4} x^{10} y^{7} } = 4 \sqrt[3]{4 x^{10} y^{7} }

Now, we have x^10, so if we divide the exponent by the root factor, we get 10/3 = 3 1/3, which means we will extract x^9 that will become x^3 outside and x will remain inside.

4 \sqrt[3]{4 x^{10} y^{7} } = 4x^{3} \sqrt[3]{4 x y^{7} }

For the y's we have y^7 inside the cubic root, that means the true exponent is y^(7/3)... so we can extract y^2 and 1 y will remain inside.

4x^{3} \sqrt[3]{4 x y^{7} } = 4x^{3} y^{2} \sqrt[3]{4 x y}

The answer is then:

4x^{3} y^{2} \sqrt[3]{4 x y} = 4x^{3} y^{2} (\sqrt[3]{4 x y})

4 0
3 years ago
Will mark brainliest
vovikov84 [41]
(0,0)-->(0,0)
(3,-1)-->(9,-3)
(3,3)-->(9,9)


so what you will plug after the dilation will be the points on the right/
hope i help
 
3 0
3 years ago
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