Find the implicit derivative $\frac{d}{dx}\left(\ln\left(x+y\right)\right)=4$

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

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Function Plot

Plotting: $y^{\prime}=4x+4y-1$

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u
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x
y
z
.
(◻)
+
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×
◻/◻
/
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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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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 (3)

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