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Published (Searched): 21st September, 2021
Last Updated: 23rd September, 2021
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1. www.khanacademy.org
Second partial derivatives (article) | Khan Academy
Added by: Malachi Schaefer
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Second partial derivatives (article) | Khan Academy

... f}{\partial \redE{y}^2} \end{aligned} ∂x∂​(∂x∂f​)∂x∂​(∂y∂f​)∂y∂​(∂x∂f​)∂y∂​(∂y∂f​)​=∂x2∂2f​=∂x∂y∂2f​=∂y∂x∂2f​=∂y2∂2f​​.
Url: https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/partial-derivative-and
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2. www.khanacademy.org
Multivariable chain rule, simple version (article) | Khan Academy
Added by: Jamiya Randolph
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Multivariable chain rule, simple version (article) | Khan Academy

\end{array} ↑ dtd​​​f(x(t),y(t))This is an ordinary derivative,not a partial derivative ∂t∂​because the total compositionhas one input and one output.​How f ...
Url: https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/differentiating-vector
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3. en.wikipedia.org
∂ - Wikipedia
Added by: Jorge Kelly
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∂ - Wikipedia

The character ∂ (Unicode: U+2202) is a stylized cursive d mainly used as a mathematical ... Not logged in; Talk · Contributions · Create account · Log in ...
Url: https://en.wikipedia.org/wiki/∂
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4. mathinsight.org
A differentiable function with discontinuous partial derivatives ...
Added by: Devon Acosta
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A differentiable function with discontinuous partial derivatives ...

An example of such a strange function is f(x,y)={(x2+y2)sin(1√x2+y2) if (x,y)≠(0 ... For example, the derivative with respect to x can be calculated by ∂f∂x(0 ...
Url: https://mathinsight.org/differentiable_function_discontinuous_partial_derivatives
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5. mathinsight.org
Directional derivative and gradient examples - Math Insight
Added by: Brenna Kidd
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Directional derivative and gradient examples - Math Insight

The partial derivatives of f at the point (x,y)=(3,2) are: ∂f∂x(x,y)=2xy∂f∂y(x ... point (3,2) in the direction of (1,2) is Duf(3,2)=12u1+9u2=12√5+18√5=30√5.
Url: https://mathinsight.org/directional_derivative_gradient_examples
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6. tutorial.math.lamar.edu
Calculus III - Chain Rule - Pauls Online Math Notes
Added by: Gina Burgess
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Calculus III - Chain Rule - Pauls Online Math Notes

So, let's start this discussion off with a function of two variables, z=f(x,y) z = f ( x , y ) . ... ∂z∂s=∂f∂x∂x∂s+∂f∂y∂y∂s∂z∂t=∂f∂x∂x∂t+∂f∂y∂y∂t ... z=e2rsin(3θ) z = e 2 r sin ⁡ ( 3 θ ) , r=st−t2 r = s t − t 2 , θ=√s2+t2 θ = s 2 + t 2 ... We connect each letter with a line and each line represents a partial ...
Url: https://tutorial.math.lamar.edu/classes/calciii/chainrule.aspx
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7. www.maths.gla.ac.uk
Partial differentiation
Added by: Lexi Stafford
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Partial differentiation

Because of this, for any given a, b, c, the graph of a function f(x, y) = c +. √ ... 1. It is important to distinguish the notation used for partial derivatives. ∂f. ∂x.
Url: http://www.maths.gla.ac.uk/~cc/2x/2005_2xnotes/2x_chap1.pdf
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8. math.libretexts.org
14.5: The Chain Rule for Multivariable Functions ...
Added by: Celeste Reese
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14.5: The Chain Rule for Multivariable Functions ...

limt→t0E(x(t),y(t))t−t0=limt→t0(E(x,y)√(x−x0)2+(y−y0)2√(x−x0)2+(y ... The first term in the equation is ∂f∂x⋅dxdt and the second term is ...
Url: https://math.libretexts.org/Bookshelves/Calculus/Book:_Calculus_(OpenStax)/14:_Differentiation_of_Functi
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9. books.google.com.ua
The Porous Medium Equation: Mathematical Theory
Added by: Matias Valencia
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The Porous Medium Equation: Mathematical Theory

... analysts' convention about the sign; in coordinates x = (x1 ,...,x d), we have ∆ g f = 1 √ |g| ∂ x i ( gij √ |g|∂ x j f) ) = gij ∂2f ∂x i x j − Γk ij gij ∂f ∂x k , where ...
Url: https://books.google.com.ua/books?id=bCfk0pKwJOUC&pg=PA269&lpg=PA269&dq=login aöf&source=bl&ots=RNLuBCa
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