Find the derivative of $\arcsin\left(\sqrt{2x}\right)$

Step-by-step Solution

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

Final answer to the problem

$\frac{\sqrt{2}}{2\sqrt{1-2x}\sqrt{x}}$
Got another answer? Verify it here!

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
  • Load more...
Can't find a method? Tell us so we can add it.
1

Taking the derivative of arcsine

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

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

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

With a free account, access a part of this solution

Unlock the first 3 steps of this solution

Learn how to solve differential calculus problems step by step online. Find the derivative of arcsin((2x)^(1/2)). Taking the derivative of arcsine. Cancel exponents \frac{1}{2} and 2. The power of a product is equal to the product of it's factors raised to the same power. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.

Final answer to the problem

$\frac{\sqrt{2}}{2\sqrt{1-2x}\sqrt{x}}$

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

Help us improve with your feedback!

Function Plot

Plotting: $\frac{\sqrt{2}}{2\sqrt{1-2x}\sqrt{x}}$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

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

How to improve your answer:

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.

Used Formulas

See formulas (3)

Your Personal Math Tutor. Powered by AI

Available 24/7, 365.

Complete step-by-step math solutions. No ads.

Includes multiple solving methods.

Download complete solutions and keep them forever.

Premium access on our iOS and Android apps.

Join 500k+ students in problem solving.

Choose your plan. Cancel Anytime.
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.

Create an Account