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Find the derivative of $\arctan\left(x-\sqrt{1+x^2}\right)$

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 Final answer to the problem

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

How should I solve this problem?

• Choose an option
• 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 arctangent

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

Learn how to solve problems step by step online.

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

Learn how to solve problems step by step online. Find the derivative of arctan(x-(1+x^2)^(1/2)). Taking the derivative of arctangent. 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 power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

 Final answer to the problem

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

 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

SnapXam A2

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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