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Find the implicit derivative $\frac{d}{dx}\left(2xy=1\right)$

Step-by-step Solution

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Solution

Formulas

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Final answer to the problem

$y+xy^{\prime}=0$
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Step-by-step Solution

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Learn how to solve product rule of differentiation problems step by step online. Find the implicit derivative d/dx(2xy=1). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the constant function (1) is equal to zero. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=y.

Final answer to the problem

$y+xy^{\prime}=0$

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Function Plot

Plotting: $y^{\prime}=\frac{-y}{x}$

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1
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5
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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

How to improve your answer:

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Main Topic: Product Rule of differentiation

The product rule is a formula used to find the derivatives of products of two or more functions. It may be stated as $(f\cdot g)'=f'\cdot g+f\cdot g'$

Used Formulas

See formulas (4)

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