Turunan: Perbedaan antara revisi
Konten dihapus Konten ditambahkan
Baris 113:
| caption2 = '''Gambar 2.''' The [[Secant line|secant]] to curve ''y''= ''f''(''x'') determined by points (''x'', ''f''(''x'')) and {{nowrap|(''x'' + ''h'', ''f''(''x'' + ''h''))}}
| image3 = Lim-secant.svg
| caption3 = '''
| image4 = Derivative GIF.gif
| caption4 = '''Gambar 4.''' Ilustrasi animasi: garis singgung (turunan) sebagai batas garis potong
Baris 120:
=== Sifat - sifat turunan ===
Linearitas
* <math>\frac{d}{dx}(u + v) = u' + v'\,</math>
* <math>\frac{d}{dx}(nu) = n\frac{du}{dx}\,</math>
Aturan produk
* <math>\frac{d}{dx}(u v) = u' v + u v'\,</math>
Dalil rantai
* <math>\frac{dy}{dx} = \frac{dy}{du}\cdot\frac{dv}{du}\cdot\frac{du}{dx}\,</math>
Sifat umum lain
▲* <math>\frac{d}{dx}(\frac{u}{v}) = \frac{u' v - u v'}{v^2}\,</math>
* <math>\frac{d}{dx}(x^n) = n x^{n-1}\,</math>
* <math>\frac{d}{dx}(u^n) = nu^{n-1}\cdot\frac{du}{dx}</math>
Baris 154 ⟶ 150:
* <math>\frac{d}{dx}(\cot{x}) = -\csc^2{x}\,</math>
* <math>\frac{d}{dx}(\sec{x}) = \sec{x} \tan{x}\,</math>
* <math>\frac{d}{dx}(\csc{x}) = -\csc{x} \cot{x}\,</math>
;Invers
Baris 168 ⟶ 164:
;Hiperbolik
* <math>\frac{d}{dx}(\sinh{x}) =
* <math>\frac{d}{dx}(\cosh{x}) = \sinh{x}\,</math>
* <math>\frac{d}{dx}(\tanh{x}) = \text{sech}^2\,{x}\,</math>
* <math>\frac{d}{dx}(\coth{x}) = -\text{csch}^2{x}\,</math>
* <math>\frac{d}{dx}(\text{sech}\,{x})= -\text{sech}\,{x}\tanh{x}</math>
* <math>\frac{d}{dx}
== Contoh soal dalam aplikasi turunan ==
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