# Step-by-step Solution

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
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\arctan\left(\sqrt{x}\right)\right)$

Learn how to solve differential calculus problems step by step online.

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

Learn how to solve differential calculus problems step by step online. Derive the function arctan(x^0.5) with respect to x. Taking the derivative of arctangent. Cancel exponents \frac{1}{2} and 2. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.

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

### Problem Analysis

$\frac{d}{dx}\left(\arctan\left(\sqrt{x}\right)\right)$

### Main topic:

Differential calculus

~ 0.05 seconds