Kuta Software - Infinite Calculus Name___________________________________ Differentiation - Quotient Rule Date________________ Period____ Differentiate each function with respect to x. 1) y = 2 2x4 − 5 3) f ( x) = 5 3 4x + 4 3x4 + 2 5) y = 3 3x − 2 7) y = 4x5 + x2 + 4 5x2 − 2 ©S w2k0b1Q3v tKWuFtWai TSJonf4tawdakrZet 5LnLsCG.j 4 vA6lOlZ 9rZi7gHhvtUsK FreecshearQvneUdL.p s NMRaYdAer MwciAtAhN 2I9nCfWianjiatSey 6CRaJlLcluTlJuAst.g 2) f ( x) = 4) y = 2 x5 − 5 4x3 − 3x2 4x5 − 4 4x5 + 2x2 6) y = 3x4 + 5 8) y = -1- 3x4 + 5x3 − 5 2x4 − 4 Worksheet by Kuta Software LLC x3 − x2 − 3 9) y = x5 + 3 10) y = x4 + 6 3 − 4x 11) y = −4 4x4 − 4x2 + 5 5 3 2x + 3 Critical thinking question: 12) A classmate claims that () f ' f' = for any functions f and g. Show an example that proves your g g' classmate wrong. ©R B2n0w1s3s PKnuytYaJ fShogfRtOwGadrTen hLyLHCB.4 s tA1lFlU 1rviOgZhJthse Tryersae6rHvzeIdJ.h W AMkaPdCeQ MwtiGtFhB dIenjfuienAietfeT XCvaTl1cwuylUuKsY.3 -2- Worksheet by Kuta Software LLC Kuta Software - Infinite Calculus Name___________________________________ Differentiation - Quotient Rule Date________________ Period____ Differentiate each function with respect to x. 1) y = 2 2x4 − 5 2) f ( x) = 2 ⋅ 8x3 dy =− dx (2 x 4 − 5) 2 16 x 3 =− 8 4 x − 20 x 4 + 25 3) f ( x) = 5 3 4x + 4 f ' ( x) = − f ' ( x) = − =− 4) y = (4 x 3 + 4) 2 15 x 2 =− 6 4x + 8x3 + 4 4x5 + x2 + 4 5x2 − 2 x 10 10 x 4 − 10 x 5 + 25 4x3 − 3x2 4x5 − 4 dy (3 x 4 + 5)(20 x 4 + 4 x) − (4 x 5 + 2 x 2 ) ⋅ 12 x 3 = dx (3 x 4 + 5) 2 12 x 8 − 12 x 5 + 100 x 4 + 20 x = 9 x 8 + 30 x 4 + 25 8) y = dy (5 x 2 − 2)(20 x 4 + 2 x) − (4 x 5 + x 2 + 4) ⋅ 10 x = dx (5 x 2 − 2) 2 60 x 6 − 40 x 4 − 44 x = 25 x 4 − 20 x 2 + 4 ©7 f2V021V3O nKMuJtCaF VSYoSfgtfwFaGrmeL 8LpLCCP.M Q mAFl7lL orxiqgDh0tpss LrFezsyeIrrvReNds.P Q uMSa0d4eL twii7t6hz YI0nsfMionEiMtzeL ECia7lDctu9lfuesU.f ( x 5 − 5) 2 4x5 + 2x2 6) y = 3x4 + 5 dy (3 x 3 − 2) ⋅ 12 x 3 − (3 x 4 + 2) ⋅ 9 x 2 = dx (3 x 3 − 2) 2 9 x 6 − 24 x 3 − 18 x 2 = 9 x 6 − 12 x 3 + 4 7) y = 2 ⋅ 5x4 dy (4 x 5 − 4)(12 x 2 − 6 x) − (4 x 3 − 3 x 2 ) ⋅ 20 x 4 = dx (4 x 5 − 4) 2 −8 x 7 + 9 x 6 − 12 x 2 + 6 x = 4 x 10 − 8 x 5 + 4 5 ⋅ 12 x 2 3x4 + 2 5) y = 3 3x − 2 2 x5 − 5 3x4 + 5x3 − 5 2x4 − 4 dy (2 x 4 − 4)(12 x 3 + 15 x 2 ) − (3 x 4 + 5 x 3 − 5) ⋅ 8 x 3 = dx (2 x 4 − 4) 2 −5 x 6 − 4 x 3 − 30 x 2 = 2x8 − 8x4 + 8 -1- Worksheet by Kuta Software LLC x3 − x2 − 3 9) y = x5 + 3 dy ( x 5 + 3)(3 x 2 − 2 x) − ( x 3 − x 2 − 3) ⋅ 5 x 4 = dx ( x 5 + 3) 2 −2 x 7 + 3 x 6 + 15 x 4 + 9 x 2 − 6 x = x 10 + 6 x 5 + 9 10) y = x4 + 6 3 − 4x −4 −4 −5 dy (3 − 4 x ) ⋅ 4 x 3 − ( x 4 + 6) ⋅ 16 x = dx (3 − 4 x −4 ) 2 12 x 11 − 32 x 7 − 96 x 3 = 9 x 8 − 24 x 4 + 16 11) y = 4x4 − 4x2 + 5 5 3 2x + 3 dy = dx = ( 5 3 ) 2 10 3 2 x + 3 (16 x − 8 x) − (4 x − 4 x + 5) ⋅ x 3 3 4 (2x + 3) 5 3 56 x 14 3 2 2 8 3 3 + 144 x − 8 x − 72 x − 50 x 12 x 10 3 2 3 5 3 + 36 x + 27 Critical thinking question: 12) A classmate claims that () f ' f' = for any functions f and g. Show an example that proves your g g' classmate wrong. Many answers. Ex: f = 4, g = 2 x, − 2 ≠0 x2 Create your own worksheets like this one with Infinite Calculus. Free trial available at KutaSoftware.com ©w M2K0G1G3Y PKKuntcat BS4oMfwt2wqa6rDe1 FLALGCh.1 u 0A6l3ly BrtikgvhitHsn yrdeEs6e2rkvbedds.K Z 3MHa2ddem JwsiGtNhv VIcnVfjisnwiKtveH eCDaWlWcruelauNsw.F -2- Worksheet by Kuta Software LLC