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Turunan dari fungsi-fungsi implisit

Turunan dari fungsi-fungsi implisit. Tim Dosen Kalkulus II. Satu variabel bebas. Jika persamaan dimana adalah fungsi dari variabel x dan yang dapat diturunkan , y adalah fungsi x, maka dimana. Contoh. Carilah dan jika. Dua variabel bebas.

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Turunan dari fungsi-fungsi implisit

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  1. Turunandarifungsi-fungsiimplisit Tim DosenKalkulus II

  2. Satuvariabelbebas • Jikapersamaandimanaadalahfungsidarivariabel x dan yang dapatditurunkan, y adalahfungsi x, maka dimana

  3. Contoh • Carilahdanjika

  4. Duavariabelbebas • Jika , dimanafungsidarivariabel-variabel x, y, dan z; z sebagaifungsidarivariabel x dan y, maka dan dimana

  5. Increment dan Total Diferensial

  6. Increment fungsiduavariabel • Jikamaka increment dinyatakan:

  7. Total diferensialfungsiduavariabel • Jikamaka total diferensial dinyatakan:

  8. Jikadananggapbahwa dapatditurunkandititikmaka dimanasehingga Maka, ketikadankecil,

  9. Increment fungsitigavariabel • Jikamaka increment dinyatakan:

  10. Total diferensialfungsitigavariabel • Jikamaka total diferensial dinyatakan:

  11. Jikadananggapbahwa dapatditurunkandititik maka dimanasehingga Maka, ketikadankecil,

  12. Increment fungsibeberapavariabel • Jikamaka increment dinyatakan:

  13. Total diferensialfungsibeberapavariabel • Jikamaka total diferensial dinyatakan:

  14. Jikadananggapbahwa dapatditurunkandititik maka dimanasehingga Maka, ketikakecil,

  15. Contoh: • Carilahdandari: 1. 2. 3.

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