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Find the derivative of $\mathrm{arcsec}\left(2x+1\right)$

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Solution

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Final answer to the problem

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

Taking the derivative of arcsecant

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

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

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Unlock the first 3 steps of this solution

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative of arcsec(2x+1). Taking the derivative of arcsecant. 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 times a constant, is equal to the constant. The derivative of the linear function is equal to 1.

Final answer to the problem

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

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Function Plot

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

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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
D□x
∫
∫◻
|◻|
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:

Similar Problems Solved

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

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

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

$\frac{d}{dx}\arcsin\left(2x-3\right)$

$\frac{d}{dx}\left(\arcsin\left(2x-5\right)\right)$

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

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

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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