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Find the derivative of $\arcsin\left(\frac{1-x^2}{1+x^2}\right)$

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Final Answer

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

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Taking the derivative of arcsine

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

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

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Learn how to solve problems step by step online. Find the derivative of arcsin((1-x^2)/(1+x^2)). Taking the derivative of arcsine. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Multiplying the fraction by -1. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}.

Final Answer

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

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Function Plot

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

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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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