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Find the derivative of $\ln\left(\arccos\left(\frac{1}{\sqrt{x}}\right)\right)$

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Final Answer

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

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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 $\displaystyle f'(x)=\frac{a'}{a}$

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

Learn how to solve differential calculus problems step by step online.

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

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Learn how to solve differential calculus problems step by step online. Find the derivative of 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. 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}. Multiplying fractions \frac{1}{\arccos\left(\frac{1}{\sqrt{x}}\right)} \times \frac{-1}{\sqrt{1-\frac{1}{x}}}.

Final Answer

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

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Find the derivativeFind derivative of lnarccos(1/(x^0.5)) using the product ruleFind derivative of lnarccos(1/(x^0.5)) using the quotient ruleFind derivative of lnarccos(1/(x^0.5)) using logarithmic differentiation

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

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7
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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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Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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