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Find the implicit derivative $\frac{d}{dx}\left(x^2+\arctan\left(y\right)=y-1\right)$

Step-by-step Solution

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Solution

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Final answer to the problem

$y^{\prime}=\frac{2x\left(1+y^2\right)}{y^2}$
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Step-by-step Solution

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Learn how to solve sum rule of differentiation problems step by step online. Find the implicit derivative d/dx(x^2+arctan(y)=y-1). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

Final answer to the problem

$y^{\prime}=\frac{2x\left(1+y^2\right)}{y^2}$

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Function Plot

Plotting: $y^{\prime}=\frac{2x\left(1+y^2\right)}{y^2}$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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:

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Main Topic: Sum Rule of Differentiation

The sum rule is a method to find the derivative of a function that is the sum of two or more functions.

Used Formulas

See formulas (5)

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