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

# Find the derivative of $\arctan\left(\sqrt{x}\right)$

## Step-by-step Solution

Go!
Math 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

###  Videos

$\frac{1}{2\left(1+x\right)\sqrt{x}}$
Got another answer? Verify it here!

##  Step-by-step Solution 

Specify the solving method

1

Taking the derivative of arctangent

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

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

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

Learn how to solve differential calculus problems step by step online. Find the derivative of arctan(x^1/2). 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}. Multiply the fraction and term.

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

##  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

Find the derivativeFind derivative of arctan(x^0.5) using the product ruleFind derivative of arctan(x^0.5) using the quotient ruleFind derivative of arctan(x^0.5) using logarithmic differentiationFind derivative of arctan(x^0.5) using the definition

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.