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Find the derivative of $\ln\left(\arctan\left(\frac{1x}{3}\right)\right)$

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Final Answer

$\frac{1}{3}\left(\frac{9}{\left(x^2+9\right)\arctan\left(\frac{x}{3}\right)}\right)$
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Step-by-step Solution

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Simplify the derivative by applying the properties of logarithms

$\frac{d}{dx}\left(\ln\left(\arctan\left(\frac{x}{3}\right)\right)\right)$

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$\frac{d}{dx}\left(\ln\left(\arctan\left(\frac{x}{3}\right)\right)\right)$

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Learn how to solve problems step by step online. Find the derivative of ln(arctan((x1)/3)). Simplify the derivative by applying the properties of logarithms. 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 arctangent. 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

$\frac{1}{3}\left(\frac{9}{\left(x^2+9\right)\arctan\left(\frac{x}{3}\right)}\right)$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of lnarctan(x1/3) using the product ruleFind derivative of lnarctan(x1/3) using the quotient ruleFind derivative of lnarctan(x1/3) using logarithmic differentiation

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Function Plot

Plotting: $\frac{1}{3}\left(\frac{9}{\left(x^2+9\right)\arctan\left(\frac{x}{3}\right)}\right)$

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1
2
3
4
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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