Partial derivative
Summary
A partial derivative of a function of several variables is its derivative with respect to one variable, while all other variables stay fixed. It measures the rate of change of the function along one coordinate axis. For , the partial derivatives are and .
What this node needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
The writing levels say how complete the text of a node is. They do not measure its truth.
What this needs
To read this node, read these 4 nodes in this order. The foundations come first, and the list ends with this node.
- no evidence level
- Euclidean space object
- Function concept
- Function of several variables concept
- Partial derivative concept
What depends on this
89 nodes use this node, directly or through other nodes.
- Exterior derivative 004FRCXH6M
- Saddle point 00N3T18QNA
- Change of variables in multiple integrals 00N5FHP1CV
- Volume of a ball in R^n 00YH28R457
- Divergence 02NSMQVQWK
- Tangent plane to a graph 035V802J58
- Chain rule for Jacobian matrices 03GGQEAG9S
- Mean value theorem in several variables 03HGK7EW6R
- Jacobian determinant 03W6Q1MFR5
- Jacobian matrix 047NDTEPCV
- Lagrange multiplier with one constraint 04A2XEX4D4
- Poincaré lemma for one-forms on convex sets 05MC3HND79
- Conservative vector field 05R9NF2J49
- Laplacian as a sum of second partial derivatives 05RCT1522R
- Jacobian of spherical coordinates 05WKRC7HWT
- Hessian matrix 0693Y2METT
- Fréchet derivative 06EH97V2A7
- Directional derivative 06KWGHDN2J
- Area of a region as a line integral 09CBQB6V67
- Higher partial derivatives 09ZXGX55DM
- Derivative gives the directional derivatives 0A6PMR20N4
- Chain rule for a composition with a curve 0A8TJ0VHC7
- Gradient 0ABK9V9Y64
- Stokes' theorem 0AKRKVHW94
- Curl-free vector field on a convex set is conservative 0B22P010D6
- Strict differentiability 0B6QWX3086
- Path independence of line integrals 0BFN21TF5F
- Tangent plane and normal vector of a surface 0BJDQ2HBH1
- Implicit function theorem 0BXBADR94C
- Harmonic function 0DEB0JMN0W
- Surface integral 0DQ8ERJZNS
- Laplacian 0E0B6RA8K0
- Orientable surface 0EKZW08FQ5
- Closed and exact forms 0F1AVGX26N
- Iterated derivative 0F32S73FJN
- Derivative vanishes at a local extremum 0F405477F8
- Divergence of a curl is zero 0F56CMMC5P
- Total derivative 0FNKFT8H6E
- Scalar potential 0FP4BVDAAQ
- Cylindrical coordinates 0G4MFRQSGN
- Derivative of the inverse function 0G65751VSW
- Curl-free field that is not conservative 0GRM3BS0DD
- Second derivative test in several variables 0GYDV9FE98
- Divergence theorem on a rectangle in the plane 0GZ3D8F921
- Del operator 0H6DP8CHND
- Scalar potential 0H7C3T1GJY
- Differentiable function of several variables 0HHHDCXZV4
- Generalised Stokes theorem 0HPHKCGEQ0
- Green's theorem 0HR3N02317
- Vector calculus identities 0JC5X4HWR2
- Saddle point 0JW6MDHAZD
- Divergence theorem 0JX86PSSA9
- Inverse function theorem 0K9HSJFCMJ
- Continuous partial derivatives imply differentiability 0KXSK8TEEB
- Diffeomorphism 0KZZ70ZHXP
- Curl of a gradient is zero 0M2JRW1J0N
- One-form 0MTENFBW3Q
- Divergence 0MWV6ZTK6S
- Implicit function theorem for a surjective derivative 0NE2W2XPQJ
- Curl 0NF6GQNXMY
- Derivative of a map into R^n by components 0NS0X75RS1
- Gradient 0NS2QYVC4Y
- Second-order Taylor expansion 0P30YYZN85
- Conservative vector field 0PKG97PX9Y
- Differential form 0QHTX7WQEY
- Implicit differentiation 0QKA345AW1
- Polar coordinates 0RJZV05MJA
- Spherical coordinates 0RW8KPMXF6
- Wedge product of forms 0S166D363M
- Gradient theorem 0SD237FEJD
- Integration in polar coordinates 0T89W1QZ9K
- Partial derivatives do not imply differentiability 0TNZC55X3J
- Lagrange multipliers 0VKKP8X6Q6
- Gradient is orthogonal to level sets 0VXYV3NQQ1
- Linear approximation 0W276SSSCG
- Harmonic function 0W5NJQ8MKY
- Volume of a ball in R^3 0WMDV48VSN
- Surface area 0WQE3G7B88
- The exterior derivative squares to zero 0X308R2DBE
- Laplacian 0XQ2ZVN1PZ
- Directional derivative 0Y7PVW4Q44
- Jacobian matrix 0YF0VXKXGB
- Flux through a surface 0YPRY7T4PK
- Homotopy invariance of line integrals of closed forms 0YVVN6R715
- Tangent plane to a graph 0YXEHVA93R
- Diffeomorphism 0Z1Y7JHGBR
- Local homeomorphism from the inverse function theorem 0Z8CSYVHDJ
- Gradient points in the direction of steepest ascent 0ZC78099PA
- Jacobian determinant 0ZCSMYHTBP
Sources
- Web https://en.wikipedia.org/wiki/Partial_derivative, lead section
What links here
Used by
- Jacobian matrix 047NDTEPCV
- Directional derivative 06KWGHDN2J
- Higher partial derivatives 09ZXGX55DM
- Derivative gives the directional derivatives 0A6PMR20N4
- Gradient 0ABK9V9Y64
- Continuous partial derivatives imply differentiability 0KXSK8TEEB
- Divergence 0MWV6ZTK6S
- Curl 0NF6GQNXMY
- Gradient 0NS2QYVC4Y
- Partial derivatives do not imply differentiability 0TNZC55X3J
- Directional derivative 0Y7PVW4Q44
- Jacobian matrix 0YF0VXKXGB
- Tangent plane to a graph 0YXEHVA93R
Definitions
- Partial derivative 05AXG3QRKR