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Find the implicit derivative $\frac{d}{dx}\left(y^3-2y+3x^3=4x+1\right)$

Step-by-step Solution

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Final Answer

$y^{\prime}=\frac{4-9x^{2}}{3y^2-2}$
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Step-by-step Solution

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

$\frac{d}{dx}\left(y^3-2y+3x^3\right)=\frac{d}{dx}\left(4x+1\right)$

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$\frac{d}{dx}\left(y^3-2y+3x^3\right)=\frac{d}{dx}\left(4x+1\right)$

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Learn how to solve problems step by step online. Find the implicit derivative d/dx(y^3-2y3x^3=4x+1). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the constant function (1) is equal to zero.

Final Answer

$y^{\prime}=\frac{4-9x^{2}}{3y^2-2}$

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Function Plot

Plotting: $y^{\prime}=\frac{4-9x^{2}}{3y^2-2}$

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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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