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

## Step-by-step Solution

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### Videos

$y^{\prime}=\frac{2xy^2\sqrt{x+y}-\frac{1}{2}}{\frac{1}{2}-2x^2y\sqrt{x+y}}$
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## Step-by-step Solution

Problem to solve:

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

Specify the solving method

1

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

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

Learn how to solve implicit differentiation problems step by step online.

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

Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative (d/dx)((x+y)^1/2=1+x^2y^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}. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the linear function is equal to 1.

$y^{\prime}=\frac{2xy^2\sqrt{x+y}-\frac{1}{2}}{\frac{1}{2}-2x^2y\sqrt{x+y}}$
SnapXam A2

### beta Got another answer? Verify it!

Go!
1
2
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4
5
6
7
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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
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

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

### Main topic:

Implicit Differentiation

~ 0.25 s