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Find the derivative of $\ln\left(x^2+1\right)^2$

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$\frac{4x\ln\left(x^2+1\right)}{x^2+1}$
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 Step-by-step Solution 

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1

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

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

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

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

Learn how to solve differential calculus problems step by step online. Find the derivative of ln(x^2+1)^2. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. 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}. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the constant function (1) is equal to zero.

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

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Find the derivativeFind derivative of ln(x^2+1)^2 using the product ruleFind derivative of ln(x^2+1)^2 using the quotient ruleFind derivative of ln(x^2+1)^2 using logarithmic differentiationFind derivative of ln(x^2+1)^2 using the definition

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Go!
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

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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