ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

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

Go!
Symbolic mode
Text mode
Go!
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

## Derivatives of inverse trigonometric functions

$\frac{d}{dx}\left(\arctan\left(\theta \right)\right)=\frac{1}{1+\theta ^2}\frac{d}{dx}\left(\theta \right)$

## Basic Derivatives

· Sum Rule for Differentiation
$\frac{d}{dx}\left[f\left(x\right)+g\left(x\right)\right]=\frac{d}{dx}f\left(x\right) + \frac{d}{dx}g\left(x\right)$
· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$
$\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)$
· Power rule for derivatives
$\frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right)$
· Derivative of a Constant
$\frac{d}{dx}\left(c\right)=0$

SnapXam A2

Go!
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

###  Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.