Find the implicit derivative of $-x^2+y^2=\left(2x^2+2y^{\left(2-x\right)}\right)^2$

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Final answer to the problem

$-2x+2y\cdot y^{\prime}=2\left(2x^2+2y^{\left(2-x\right)}\right)\left(4x+\frac{-2y^{\left(2-x\right)}\ln\left(y^{\left(2-x\right)}\right)}{-1+x}\right)$
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Step-by-step Solution

How should I solve this problem?

  • Solve by implicit differentiation
  • Find the derivative using the definition
  • Exact Differential Equation
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  • Homogeneous Differential Equation
  • Find the derivative using the product rule
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
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1

Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable

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

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

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

Final answer to the problem

$-2x+2y\cdot y^{\prime}=2\left(2x^2+2y^{\left(2-x\right)}\right)\left(4x+\frac{-2y^{\left(2-x\right)}\ln\left(y^{\left(2-x\right)}\right)}{-1+x}\right)$

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Function Plot

Plotting: $-2x+2y\cdot y^{\prime}=2\left(2x^2+2y^{\left(2-x\right)}\right)\left(4x+\frac{-2y^{\left(2-x\right)}\ln\left(y^{\left(2-x\right)}\right)}{-1+x}\right)$

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7
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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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