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←Membuat halaman berisi '{{Calculus |Diferensial}} '''Notasi untuk diferensiasi''' tidak seragam dalam kalkulus diferensial, karena ada beberapa notasi untuk derivatif suatu fungsi (...'
 
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{{-}}TheNotasi originalasli notationyang employeddigunakan byoleh [[Gottfried Leibniz]] isbiasa useddipakai throughoutdalam mathematics[[matematika]]. It is particularly common when theUmumnya equationpersamaan {{math|''y'' {{=}} ''f''(''x'')}} isdianggap regardedsebagai ashubungan afungsional functional relationship betweenantara [[:en:dependent and independent variables|variabel dependen]] {{math|''y''}} anddan variabel independen {{math|''x''}}. In this case theDalam derivativehal canini beturunannya writtendapat asditulis:
 
: <math>\frac{dy}{dx}</math>
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Other notations can be found in various subfields of mathematics, physics, and engineering, see for example the [[Maxwell relations]] of [[thermodynamics]]. The symbol <math>\left(\frac{\partial T}{\partial V}\right)_S </math> is the derivative of the temperature ''T'' with respect to the volume ''V'' while keeping constant the entropy ''S'', while <math>\left(\frac{\partial T}{\partial V}\right)_P </math> is the derivative of the temperature with respect to the volume while keeping constant the pressure ''P''.
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== Notasi dalam kalkulus vektor ==
 
[[VectorKalkulus calculusvektor]] concernsberfokus pada [[derivativederivatif|differentiationdiferensiasi]] anddan [[integral|integrationintegrasi]] ofsuatu [[:en:vector field|vectorbidang vektor]] oratau [[:en:scalar fields|scalarskalar]] fieldssecara particularlykhusus indalam a three-dimensionalsuatu [[:en:Euclidean space|ruang Euklidean]] tiga dimensi, anddan usesmenggunakan specificnotasi notationskhusus ofuntuk differentiationdiferensiasi. Dalam In asuatu [[Cartesiansistem koordinat coordinateKartesius]] o-''xyz'', assumingyang amelambangkan [[:en:vector field|bidang vektor]] '''A''' isditulis <math>\mathbf{A} = (\mathbf{A}_x, \mathbf{A}_y, \mathbf{A}_z)</math>, and adan [[:en:scalar fieldfields|bidang skalar]] <math>\varphi</math> isditulis <math>\varphi = f(x,y,z)\,</math>.▼
== Notation in vector calculus ==
 
▲[[Vector calculus]] concerns [[derivative|differentiation]] and [[integral|integration]] of [[vector field|vector]] or [[scalar fields|scalar]] fields particularly in a three-dimensional [[Euclidean space]], and uses specific notations of differentiation. In a [[Cartesian coordinate]] o-''xyz'', assuming a [[vector field]] '''A''' is <math>\mathbf{A} = (\mathbf{A}_x, \mathbf{A}_y, \mathbf{A}_z)</math>, and a [[scalar field]] <math>\varphi</math> is <math>\varphi = f(x,y,z)\,</math>.
 
FirstPertama, a differentialsebuah operator diferensial, oratau asuatu [[:en:Hamilton operator|operator Hamilton]] [[:en:nabla symbol|∇]] whichyang isjuga calleddisebut [[:en:del|del]] is symbolically defined in thememuat formperlambangan ofdefinisi asuatu vectorvektor,
 
:<math>\nabla = \left( \frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z} \right),</math>
 
wheredimana the terminologyistilah ''symbolicallyperlambangan'' reflectsini thatmencerminkan thebahwa operator ∇ will also bejuga treateddiperlakukan assebagai ansuatu ordinaryvektor vectorbiasa.
 
<div style="float:right; margin: 0 0 10px 10px; padding:30px; font-size:500%; font-family:Times New Roman, serif; background-color: #ddddff; border: 1px solid #aaaaff;">∇''φ''</div>
* '''[[GradientGradien]]''': The gradientgradien <math>\mathrm{grad\,} \varphi\,</math> ofdari thebidang scalar fieldskalar <math>\varphi</math> isadalah asebuah vectorvektor, whichyang isditulis symbolicallydengan expressed by theperlambangan [[multiplicationperkalian]] of ∇ anddan scalarbidang fieldskalar ''<math>\varphi</math>'',
 
::<math>
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<div style="float:right; margin: 0 0 10px 10px; padding:30px; font-size:500%; font-family: Serif; background-color: #ddddff; border: 1px solid #aaaaff;">∇∙'''A'''</div>
* '''[[Divergence]]''': The divergencedivergensi <math>\mathrm{div}\,\mathbf{A}\,</math> ofdari thebidang vector fieldvektor '''A''' isadalah asuatu scalarskalar, whichyang isditulis symbolicallydengan expressed by theperlambangan [[dotproduk productskalar]] of ∇ and thedan vectorvektor '''A''',
 
:: <math>
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<div style="float:right; margin: 0 0 0px 0px; padding:10px 30px 30px 30px; font-size:500%; font-family: Times New Roman, serif; background-color: #ddddff; border: 1px solid #aaaaff;">∇<sup>2</sup>''φ''</div>
* '''[[Laplacian]]''': The Laplacian <math>\operatorname{div} \operatorname{grad} \varphi</math> ofsebuah thebidang scalar fieldskalar <math>\varphi</math> isadalah asuatu scalarskalar, whichyang isditulis symbolicallydengan expressedperlambangan byperkalian the scalar multiplication ofskalar ∇<sup>2</sup> and thedan scalarbidang fieldskalar ''φ'',
 
:: <math>
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\end{align}
</math>
:: wheredi mana, <math>\Delta = \nabla^2</math> is called adisebut [[:en:Laplacian operator|operator Laplacian]].
 
<div style="float:right; margin: 0 0 10px 10px; padding:30px; font-size:500%; font-family: Serif; background-color: #ddddff; border: 1px solid #aaaaff;">∇×'''A'''</div>
* '''[[:en:Curl (mathematics)|RotationRotasi]]''': The rotationrotasi <math>\mathrm{curl}\,\mathbf{A}\,</math>, oratau <math>\mathrm{rot}\,\mathbf{A}\,</math>, ofsebuah thebidang vector fieldvektor '''A''' isadalah asuatu vectorvektor, whichyang isditulis symbolicallydengan expressed by theperlambangan [[crossproduk productsilang]] of ∇ and thedan vectorvektor '''A''',
 
:: <math>
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</math>
 
Banyak operasi turunan simbolis dapat digeneralisasi langsung dengan operator gradian dalam [[sistem koordinat Kartesius]]. Misalnya, [[kaidah hasil kali]] dengan variabel tunggal mempunyai analog langsung dalam perkalian bidang skalar melalui penggunaan operator gradien, sebagaimana dalam
Many symbolic operations of derivatives can be generalized in a straightforward manner by the gradient operator in Cartesian coordinates. For example, the single-variable [[product rule]] has a direct analogue in the multiplication of scalar fields by applying the gradient operator, as in
 
:<math>(f g)' = f' g+f g' ~~~ \Longrightarrow ~~~ \nabla(\phi \psi) = (\nabla \phi) \psi + \phi (\nabla \psi).</math>
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Further notations have been developed for more exotic types of spaces. For calculations in [[Minkowski space]], the [[D'Alembert operator]], also called the D'Alembertian, wave operator, or box operator is represented as <math>\Box</math>, or as <math>\Delta</math> when not in conflict with the symbol for the Laplacian.
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