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Find the implicit derivative $\frac{d}{dx}\left(4x^3+7xy^2=2y^3\right)$

Step-by-step Solution

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Final Answer

$y^{\prime}=\frac{-12x^{2}-7y^2}{2\left(7x-3y\right)y}$
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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

$\frac{d}{dx}\left(4x^3+7xy^2\right)=\frac{d}{dx}\left(2y^3\right)$

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$\frac{d}{dx}\left(4x^3+7xy^2\right)=\frac{d}{dx}\left(2y^3\right)$

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Learn how to solve problems step by step online. Find the implicit derivative d/dx(4x^3+7xy^2=2y^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 (2) is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of the linear function is equal to 1.

Final Answer

$y^{\prime}=\frac{-12x^{2}-7y^2}{2\left(7x-3y\right)y}$

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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
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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