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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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True or false X times X times X times X times X equals 5X
nevsk [136]

Answer:

false

Step-by-step explanation:

X times X times X times X times X equals X^5 not 5X

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3 years ago
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18. WILL MARK BRAINLIEST!!HELP! ​
vagabundo [1.1K]

Answer:

3x-20

Step-by-step explanation:

5 0
3 years ago
Hi, does anyone know the answer to this question? I’m bad at geometry and I’m struggling to answer it.
arsen [322]

Answer:

QT = 16

Step-by-step explanation:

ΔQRS ~ ΔQRT

In similar triangles, corresponding angles are in same ratio.

\frac{QS}{QR}=\frac{QR}{QT}\\\\\frac{25}{20}=\frac{20}{QT}

Cross multiply,

QT * 25 = 20 * 20

QT =\frac{20*20}{25}\\\\QT = 4*4\\\\QT = 16

3 0
3 years ago
What’s the answer to the top question and steps how to solve?
Leviafan [203]

Answer:

-3.69

Step-by-step explanation:

Exponential equations can be solved by taking Ln (natural logarithm) of both sides. The rule we need to know is:

Ln(a^b)=bLn(a)

Now lets work out this problem:

16^{2x+3}=13^{x-1}\\Ln(16^{2x+3})=Ln(13^{x-1})\\(2x+3)Ln(16)=(x-1)Ln(13)

Using calculator, we take the values of Ln 16 and Ln 13 as:

Ln 16 = 2.7726

Ln 13 = 2.5649

Now, we can solve for x:

(2x+3)Ln(16)=(x-1)Ln(13)\\(2x+3)2.7726=(x-1)2.5649\\5.5452x+8.3178=2.5649x-2.5649\\2.9803x=-10.8827\\x=-3.69

x is -3.69 (rounded to 2 decimal places)

3 0
3 years ago
Help me answer this please
Marizza181 [45]

Answer:

77 feet below sea level.

Step-by-step explanation:

Since y is the time the submarine is ascending, we can plug it in for y and find our answer. We can create an equation where D is the depth and y is time ascending: D = -230 + 17y

Substitute 9 for y:

D = -230 + 17(9)

D = -230 + 153

D = -77

The depth of the submarine after 9 minutes will be 77 feet below sea level. Hope this helps, and Brainly will be highly appreciated.

7 0
2 years ago
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