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

Step-by-step Solution

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acosh
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Final answer to the problem

$\arcsin\left(2x\right)+\frac{2x}{\sqrt{1-4x^2}}$
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Step-by-step Solution

How should I solve this problem?

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  • 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

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=\arcsin\left(2x\right)$

Learn how to solve inverse trigonometric functions differentiation problems step by step online.

$\frac{d}{dx}\left(x\right)\arcsin\left(2x\right)+x\frac{d}{dx}\left(\arcsin\left(2x\right)\right)$

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Learn how to solve inverse trigonometric functions differentiation problems step by step online. Find the derivative of xarcsin(2x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\arcsin\left(2x\right). The derivative of the linear function is equal to 1. Taking the derivative of arcsine. The power of a product is equal to the product of it's factors raised to the same power.

Final answer to the problem

$\arcsin\left(2x\right)+\frac{2x}{\sqrt{1-4x^2}}$

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Function Plot

Plotting: $\arcsin\left(2x\right)+\frac{2x}{\sqrt{1-4x^2}}$

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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

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