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Find the implicit derivative $\frac{d}{dx}\left(x^2-3xy+y^2=12\right)$

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Solution

Formulas

Videos

Implicit differentiation | Advanced derivatives | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=mSVrqKZDRF4

Implicit Differentiation - Find The First &amp; Second Derivatives

https://www.youtube.com/watch?v=-XQDh6Z6DPI

Calculus - Find the derivative of natural logarithm using product property, d(ln(2x))/dx

https://www.youtube.com/watch?v=urYZhqwUTI0

Worked example: Evaluating derivative with implicit differentiation | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=KyYC8XzKsHU

Calculus - Using the power rule of logarithms to take the derivative of a natural log, d(ln(x^2))/dx

https://www.youtube.com/watch?v=JIq0y4ST7tc

Implicit differentiation with the chain rule and in

https://www.youtube.com/watch?v=TNy-IxD15f0

Function Plot

Plotting: $2x-3y-3xy^{\prime}+2y\cdot y^{\prime}=0$

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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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Similar Problems Solved

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(x^3-3x^2y+2xy^2=12\right)$

Find the derivative

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

Find the derivative

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

Find the derivative

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

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(x^2-y^2=25\right)$

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

See formulas (6)

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