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Find the implicit derivative $\frac{d}{dx}\left(2\left(x^2+y^2\right)^2=25\left(x^2-y^2\right)\right)$

Step-by-step Solution

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Solution

Final Answer

$y^{\prime}=\frac{-4x^{3}-4y^2x+25x}{\left(4x^2+4y^2+25\right)y}$
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Step-by-step Solution

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

$\frac{d}{dx}\left(2\left(x^2+y^2\right)^2\right)=\frac{d}{dx}\left(25\left(x^2-y^2\right)\right)$

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$\frac{d}{dx}\left(2\left(x^2+y^2\right)^2\right)=\frac{d}{dx}\left(25\left(x^2-y^2\right)\right)$

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Learn how to solve problems step by step online. Find the implicit derivative d/dx(2(x^2+y^2)^2=25(x^2-y^2)). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of a function multiplied by a constant (2) is equal to the constant times the derivative of the function. The derivative of a function multiplied by a constant (25) is equal to the constant times the derivative of the 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

$y^{\prime}=\frac{-4x^{3}-4y^2x+25x}{\left(4x^2+4y^2+25\right)y}$

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Function Plot

Plotting: $y^{\prime}=\frac{-4x^{3}-4y^2x+25x}{\left(4x^2+4y^2+25\right)y}$

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1
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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
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

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