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

Step-by-step Solution

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Final answer to the problem

$\frac{2x}{\sqrt{1-x^{4}}}$
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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
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1

Taking the derivative of arcsine

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

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

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Learn how to solve problems step by step online. Find the derivative of arcsin(x^2). Taking the derivative of arcsine. Simplify \left(x^2\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals 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.

Final answer to the problem

$\frac{2x}{\sqrt{1-x^{4}}}$

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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

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Function Plot

Plotting: $\frac{2x}{\sqrt{1-x^{4}}}$

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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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