Find the implicit derivative $\frac{d}{dx}\left(\cos\left(y\right)=\frac{x}{3}\right)$

Step-by-step Solution

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Solving: $\frac{d}{dx}\left(\cos\left(y\right)=\frac{x}{3}\right)$

Final answer to the problem

$y^{\prime}=\frac{-\csc\left(y\right)}{3}$
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Step-by-step Solution

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  • 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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$\frac{d}{dx}\left(\cos\left(y\right)\right)=\frac{d}{dx}\left(\frac{x}{3}\right)$

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Learn how to solve problems step by step online. Find the implicit derivative d/dx(cos(y)=x/3). 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 (\frac{1}{3}) is equal to the constant times the derivative of the function. The derivative of the linear function is equal to 1. The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x).

Final answer to the problem

$y^{\prime}=\frac{-\csc\left(y\right)}{3}$

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Function Plot

Plotting: $y^{\prime}=\frac{-\csc\left(y\right)}{3}$

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1
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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

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