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Tugas 1 Matematika 2
1.
TUGAS 1 MATEMATIKA 2 Nama
: Cinjy Saylendra Monica Prodi : Teknik Elektronika Kelas : 1E A Semester : 2 (Dua) Tahun Ajaran : 2014/2015 Soal : 1. 𝑦 = 𝑥7 + 6𝑥5 + 12𝑥3 2. 𝑦 = 𝑥−5 + 2𝑥−3 + 3𝑥−7 3. 𝑦 = √ 𝑥2 + √ 𝑥73 4. 𝑦 = 2 √𝑥 + 6 √𝑥3 5. 𝑦 = 𝑥2 .sin 2𝑥 6. 𝑦 = ( 𝑥2 + 1).cos 3𝑥 7. 𝑦 = sin 5𝑥 . tan2𝑥 8. 𝑦 = cos 3𝑥 . cot 4𝑥 9. 𝑦 = sin 5𝑥 cos7𝑥 10. 𝑦 = cos6𝑥 tan 2𝑥 Jawaban : 1. 𝑦′ = 7𝑥6 + 30𝑥4 + 36𝑥2 2. 𝑦′ = −5𝑥−6 −6𝑥−4 −21𝑥−8 3. 𝑦 = 𝑥 2 2 + 𝑥 7 3 𝑦 = 𝑥 + 𝑥 7 3
2.
𝑦′ = 1 + 7 3 𝑥 7 3 − 3 3
= 1 + 7 3 𝑥 4 3 𝑦′ = 1 + 7 3 √ 𝑥43 4. 𝑦 = 2 𝑥 1 2 + 6 𝑥 3 2 𝑦 = 2𝑥− 1 2 + 6𝑥− 3 2 𝑦′ = 2.− 1 2 . 𝑥− 1 2 − 2 2 + 6.− 3 2 . 𝑥− 3 2 − 2 2 𝑦′ = −𝑥− 3 2−9𝑥− 5 2 = − 1 𝑥 3 2 − 9 𝑥 5 2 𝑦′ = − 1 √ 𝑥3 − 9 √ 𝑥5 5. 𝑢 = 𝑥2 → 𝑢′ = 2𝑥 𝑣 = sin 2𝑥 → 𝑣′ = 2. cos 𝑥 𝑦′ = 𝑢′ . 𝑣 + 𝑢. 𝑣′ 𝑦′ = 2𝑥. sin 2𝑥 + 𝑥2 .2. cos 𝑥 𝑦′ = 2𝑥. sin 2𝑥 + 2𝑥2 .cos 𝑥 6. 𝑢 = 𝑥2 + 1 → 𝑢′ = 2𝑥 𝑣 = cos 3𝑥 → 𝑣′ = −3.sin 3𝑥 𝑦′ = 𝑢′ . 𝑣 + 𝑢. 𝑣′ 𝑦′ = 2𝑥. cos 3𝑥 + ( 𝑥2 + 1).−3.sin 3𝑥 𝑦′ = 2𝑥. cos 3𝑥 + (−3𝑥2 − 3).sin 3𝑥 7. 𝑢 = sin 5𝑥 → 𝑢′ = 5.cos 5𝑥 𝑣 = tan 2𝑥 → 𝑣′ = 2. 𝑠𝑒𝑐2 2𝑥 𝑦′ = 𝑢′ . 𝑣 + 𝑢. 𝑣′ 𝑦′ = 5. cos 5𝑥 . tan 2𝑥 + sin 5𝑥 .2. 𝑠𝑒𝑐2 2𝑥 𝑦′ = 5.cos 5𝑥. tan 2𝑥 + 2. sin5𝑥 . 𝑠𝑒𝑐2 2𝑥 8. 𝑢 = cos 3𝑥 → 𝑢′ = −3. sin3𝑥 𝑣 = cot4𝑥 → 𝑣′ = −4. 𝑐𝑠𝑐2 4𝑥 𝑦′ = 𝑢′ . 𝑣 + 𝑢. 𝑣′ 𝑦′ = −3. sin3𝑥 . cot 4𝑥 + cos 3𝑥 . −4. 𝑐𝑠𝑐2 4𝑥
3.
𝑦′ = −3.sin 3𝑥
. cot4𝑥 − 4. cos 3𝑥 . 𝑐𝑠𝑐2 4𝑥 9. 𝑢 = sin 5𝑥 → 𝑢′ = 5.cos 5𝑥 𝑣 = cos 7𝑥 → 𝑣′ = −7.sin 7𝑥 𝑦′ = 𝑢′ . 𝑣 − 𝑢. 𝑣′ 𝑣2 𝑦′ = 5. cos 5𝑥 . cos 7𝑥 − sin 5𝑥 . −7.sin 7𝑥 (cos 7𝑥)2 𝑦′ = 5.cos 5𝑥. cos 7𝑥 + 7.sin 5𝑥 . sin7𝑥 𝑐𝑜𝑠27𝑥 10. 𝑢 = cos 6𝑥 → 𝑢′ = −6. sin6𝑥 𝑣 = tan 2𝑥 → 𝑣′ = 2. 𝑠𝑒𝑐2 2𝑥 𝑦′ = 𝑢′ . 𝑣 − 𝑢. 𝑣′ 𝑣2 𝑦′ = −6. sin6𝑥. tan 2𝑥 − cos 6𝑥. 2. 𝑠𝑒𝑐2 2𝑥 (tan 2𝑥)2 𝑦′ = −6.sin 6𝑥. tan 2𝑥 − 2.cos 6𝑥. 𝑠𝑒𝑐2 2𝑥 𝑡𝑎𝑛22𝑥
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