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Find the derivative of $\frac{1}{2}\ln\left(\frac{x}{2+\sqrt{x^2+4}}\right)$

Step-by-step Solution

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Final Answer

$\frac{1}{x\sqrt{x^2+4}}$
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Step-by-step Solution

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Simplify the derivative by applying the properties of logarithms

$\frac{d}{dx}\left(\frac{1}{2}\left(\ln\left(x\right)-\ln\left(2+\sqrt{x^2+4}\right)\right)\right)$

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$\frac{d}{dx}\left(\frac{1}{2}\left(\ln\left(x\right)-\ln\left(2+\sqrt{x^2+4}\right)\right)\right)$

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Learn how to solve problems step by step online. Find the derivative of 1/2ln(x/(2+(x^2+4)^1/2)). Simplify the derivative by applying the properties of logarithms. The derivative of a function multiplied by a constant (\frac{1}{2}) is equal to the constant times the derivative of the function. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (-1) is equal to the constant times the derivative of the function.

Final Answer

$\frac{1}{x\sqrt{x^2+4}}$

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Function Plot

Plotting: $\frac{1}{x\sqrt{x^2+4}}$

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1
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5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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