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DIFERENSIAL FUNGSI SEDERHANA ( ORDINARY DIFFERENTIAL)

DIFERENSIAL FUNGSI SEDERHANA ( ORDINARY DIFFERENTIAL). Segaf , SE.MSc. Aljabar Kalkulus. Berisi Difensiasi & Integral  perubahan kecil dalam variabel sebuah fungsi . (small changes of variables at a function)

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DIFERENSIAL FUNGSI SEDERHANA ( ORDINARY DIFFERENTIAL)

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  1. DIFERENSIAL FUNGSI SEDERHANA(ORDINARY DIFFERENTIAL) Segaf, SE.MSc.

  2. AljabarKalkulus • BerisiDifensiasi & Integral  perubahankecildalamvariabelsebuahfungsi. (small changes of variables at a function) • Diferensiasi & integral adalahduaoperasimatematisberkebalikan ( two operation in vice versa or in an opposite) • Diferensiasi  penentuantingkatperubahansuatufungsi, • Integral  pembentukanpersamaansuatufungsijikaperubahannyadiketahui. • Sedangkan “Limit”  akardarikalkulus (root of calculus).

  3. PersamaanDiferensialDifferential Equation • PersamaanDiferensialadalahsuatupersamaan yang meliputiturunanfungsidarisatuataulebihvariabelterikatterhadapsatuataulebihvariabelbebas. • (A differential equation is any equation which contains derivatives, either ordinary derivatives or partial derivatives.) • Selanjutnyajikadalampersamaantersebutturunanfungsiituhanyatergantungpadasatuvariabelbebas, makadisebutPersamaanDiferensialBiasa (PDB) danbilatergantungpadalebihdarisatuvariabelbebasdisebutPersamaanDiferensialParsial (PDP).

  4. AturanTurunan (1)Derivative Rules (1)

  5. AturanTurunan (2)Derivative Rules (2)

  6. Contoh Derivative Rules • Fungsikonstan (Constant Function Rule) Jikay = k, dimana k adalahkonstanta, makady/dx = 0 contoh : y = 5  dy/dx = 0 • Fungsipangkat (Power Function Rule) Jikay = xn, dimananadalahkonstanta, makady/dx = nxn-1 contoh : y=x3dy/dx=3x3-1=3x2

  7. 3. Diferensiasiperkaliankonstantadenganfungsi Jikay = kv, dimanav = h(x),  dy/dx = k dv/dx contoh : y = 5x3  dy/dx = 5(3x2) = 15x2 4. Diferensiasipembagiankonstantadenganfungsi jikay = k/v, dimana v=h(x),maka :

  8. 5. Diferensiasipenjumlahan (pengurangan) fungsi jika y = u + v, dimana u = g(x) dan v = h(x) makady/dx = du/dx+dv/dx contoh : y = 4x2 + x3  u = 4x2 du/dx = 8x  v = x3dv/dx = 3x2 dy/dx =du/dx + dv/dx = 8x + 3x2 6. Diferensiasiperkalianfungsi Jika y = uv, dimana u = g(x) dan v = h(x)

  9. 7. Diferensiasipembagianfungsi Jikay = u/v. dimana u = g(x) dan v = h(x)

  10. 8. DiferensiasiFungsikomposit Jika y=f(u) sedangkan u=g(x),dengan bentuk lain y=f{g(x)}, maka :

  11. 9. Diferensiasifungsiberpangkat Jika y=un, dimana u=g(x) dan n adalahkonstanta, makady/dx =nun-1 .(du/dx) Contoh :

  12. exercise

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