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Algebra Baldor
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Find the derivative of $\ln\left(\frac{1+\arccos\left(x\right)}{1-\arccos\left(x\right)}\right)$

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Solution

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Final answer to the problem

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

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  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using the quotient 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
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Simplify the derivative by applying the properties of logarithms

Learn how to solve logarithmic differentiation problems step by step online.

$\frac{d}{dx}\left(\ln\left(1+\arccos\left(x\right)\right)-\ln\left(1-\arccos\left(x\right)\right)\right)$

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Learn how to solve logarithmic differentiation problems step by step online. Find the derivative of ln((1+arccos(x))/(1-arccos(x))). Simplify the derivative by applying the properties of logarithms. 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 is equal to the constant times the derivative of the function. 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}.

Final answer to the problem

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

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Function Plot

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

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0
a
b
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d
f
g
m
n
u
v
w
x
y
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.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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

How to improve your answer:

Similar Problems Solved

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$\frac{d}{dx}\left(x^{2x}\right)$

Main Topic: Logarithmic Differentiation

The logarithmic derivative of a function f(x) is defined by the formula f'(x)/f(x).

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