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

Step-by-step Solution

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asinh
acosh
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acoth
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Final Answer

$y^{\prime}=\frac{-y}{x}$
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Step-by-step Solution

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1

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

$\frac{d}{dx}\left(2e^{xy}\right)=\frac{d}{dx}\left(1\right)$

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

$\frac{d}{dx}\left(2e^{xy}\right)=\frac{d}{dx}\left(1\right)$

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Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative d/dx(2e^(xy)=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 (2) is equal to the constant times the derivative of the function. Applying the derivative of the exponential function.

Final Answer

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

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Function Plot

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

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Got a different answer? Verify it!

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1
2
3
4
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
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

How to improve your answer:

Main Topic: Implicit Differentiation

Implicit differentiation makes use of the chain rule to differentiate implicitly defined functions. For differentiating an implicit function y(x), defined by an equation R(x, y) = 0, it is not generally possible to solve it explicitly for y(x) and then differentiate. Instead, one can differentiate R(x, y) with respect to x and y and then solve a linear equation in dy/dx for getting explicitly the derivative in terms of x and y.

Used Formulas

4. See formulas

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