Find the derivative $\frac{d}{dx}\left(\ln\left(e^{4x}-1\right)-\ln\left(e^{4x}+1\right)\right)$ using the sum rule

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Final answer to the problem

$\frac{8e^{4x}}{e^{8x}-1}$
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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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The derivative of a sum of two or more functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(\ln\left(e^{4x}-1\right)\right)+\frac{d}{dx}\left(-\ln\left(e^{4x}+1\right)\right)$

Learn how to solve sum rule of differentiation problems step by step online.

$\frac{d}{dx}\left(\ln\left(e^{4x}-1\right)\right)+\frac{d}{dx}\left(-\ln\left(e^{4x}+1\right)\right)$

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Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(ln(e^(4x)-1)-ln(e^(4x)+1)) using the sum rule. 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}. Multiplying the fraction by -1.

Final answer to the problem

$\frac{8e^{4x}}{e^{8x}-1}$

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Function Plot

Plotting: $\frac{8e^{4x}}{e^{8x}-1}$

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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

How to improve your answer:

Main Topic: Sum Rule of Differentiation

The sum rule is a method to find the derivative of a function that is the sum of two or more functions.

Used Formulas

See formulas (5)

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