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Find the derivative $\frac{d}{dx}\left(x+\frac{-4}{\sqrt{3}}\arctan\left(\frac{e^x}{\sqrt{3}}\right)\right)$ using the sum rule

Step-by-step Solution

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Final Answer

$1+\frac{-4e^x}{e^{2x}+3}$
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Step-by-step Solution

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$\frac{d}{dx}\left(x-\frac{4\sqrt{3}}{3}\arctan\left(\frac{e^x}{\sqrt{3}}\right)\right)$

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

$\frac{d}{dx}\left(x-\frac{4\sqrt{3}}{3}\arctan\left(\frac{e^x}{\sqrt{3}}\right)\right)$

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Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(x+-4/(3^1/2)arctan((e^x)/(3^1/2))) using the sum rule. Simplifying. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the linear function is equal to 1. The derivative of a function multiplied by a constant (-\frac{4\sqrt{3}}{3}) is equal to the constant times the derivative of the function.

Final Answer

$1+\frac{-4e^x}{e^{2x}+3}$

Explore different ways to solve this problem

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 (x+-4/(3^0.5)arctan((e^x)/(3^0.5))) using the product ruleFind derivative of (x+-4/(3^0.5)arctan((e^x)/(3^0.5))) using the quotient ruleFind derivative of (x+-4/(3^0.5)arctan((e^x)/(3^0.5))) using logarithmic differentiation

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Function Plot

Plotting: $1+\frac{-4e^x}{e^{2x}+3}$

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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

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

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