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Find the implicit derivative $\frac{d}{dx}\left(x^2+6xy+25y^2=25\right)$

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Solution

Formulas

Videos

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

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

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

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

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

Calculus - Take the log of both sides to find the derivative, y = (x(x^2 + 1)^2)/(sqrt(2x^2 - 1))

https://www.youtube.com/watch?v=7aF6Ck6ZRxw

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

Function Plot

Plotting: $2x+6y+6xy^{\prime}+50y\cdot y^{\prime}=0$

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◻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

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

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

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

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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