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Find the implicit derivative $\frac{d}{dx}\left(xy=\cos\left(x\right)+y\right)$

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Solving: $\frac{d}{dx}\left(xy=\cos\left(x\right)+y\right)$
Solve instead: $\frac{dy}{dx}\left(xy=\cos\left(x\right)+y\right)$

Solution

Final answer to the problem

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

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  • Choose an option
  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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1

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

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$\frac{d}{dx}\left(xy\right)=\frac{d}{dx}\left(\cos\left(x\right)+y\right)$

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Learn how to solve problems step by step online. Find the implicit derivative d/dx(xy=cos(x)+y). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=y. The derivative of the linear function is equal to 1. The derivative of a sum of two or more functions is the sum of the derivatives of each function.

Final answer to the problem

$y^{\prime}=\frac{-\left(\sin\left(x\right)+y\right)}{x-1}$

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Function Plot

Plotting: $y^{\prime}=\frac{-\left(\sin\left(x\right)+y\right)}{x-1}$

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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

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