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Find the derivative using the product rule $\frac{d}{dx}\left(\frac{\sqrt{5-2}}{2x+1}\right)$

Step-by-step Solution

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Final Answer

$\frac{-2\sqrt{3}}{\left(2x+1\right)^2}$
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$\frac{d}{dx}\left(\frac{\sqrt{3}}{2x+1}\right)$

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$\frac{d}{dx}\left(\frac{\sqrt{3}}{2x+1}\right)$

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Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx(((5-2)^1/2)/(2x+1)). Simplifying. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. The derivative of the constant function (\sqrt{3}) is equal to zero. Any expression multiplied by 0 is equal to 0.

Final Answer

$\frac{-2\sqrt{3}}{\left(2x+1\right)^2}$

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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 ((5-2)^0.5)/(2x+1) using the quotient ruleFind derivative of ((5-2)^0.5)/(2x+1) using logarithmic differentiationFind derivative of ((5-2)^0.5)/(2x+1) using the definition

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Function Plot

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

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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

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Main Topic: Product Rule of differentiation

The product rule is a formula used to find the derivatives of products of two or more functions. It may be stated as $(f\cdot g)'=f'\cdot g+f\cdot g'$

Used Formulas

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