Find the derivative using the quotient rule $\frac{d}{dx}\left(\ln\left(\arccos\left(\frac{1}{\sqrt{x}}\right)\right)\right)$

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Final answer to the problem

$\frac{1}{2\sqrt{1+\frac{-1}{x}}\sqrt{x^{3}}\arccos\left(\frac{1}{\sqrt{x}}\right)}$
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Step-by-step Solution

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  • Find the derivative using the quotient rule
  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
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The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$

$\frac{1}{\arccos\left(\frac{1}{\sqrt{x}}\right)}\frac{d}{dx}\left(\arccos\left(\frac{1}{\sqrt{x}}\right)\right)$

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$\frac{1}{\arccos\left(\frac{1}{\sqrt{x}}\right)}\frac{d}{dx}\left(\arccos\left(\frac{1}{\sqrt{x}}\right)\right)$

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Learn how to solve problems step by step online. Find the derivative using the quotient rule d/dx(ln(arccos(1/(x^(1/2))))). The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. Taking the derivative of arccosine. Multiplying fractions \frac{1}{\arccos\left(\frac{1}{\sqrt{x}}\right)} \times \frac{-1}{\sqrt{1-\left(\frac{1}{\sqrt{x}}\right)^2}}. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}.

Final answer to the problem

$\frac{1}{2\sqrt{1+\frac{-1}{x}}\sqrt{x^{3}}\arccos\left(\frac{1}{\sqrt{x}}\right)}$

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Plotting: $\frac{1}{2\sqrt{1+\frac{-1}{x}}\sqrt{x^{3}}\arccos\left(\frac{1}{\sqrt{x}}\right)}$

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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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