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Tugas Matematika 1 - Semester 2 - Polman Babel
1.
Nama :Miza Pisari NPM
: 0031417 Kelas : 1 Elektronika A Tugas : MATEMATIKA Carilah nilai turunan dari fungsi berikut ini. 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). cos3𝑥 7. 𝑦 = sin 5𝑥 . tan 2𝑥 8. 𝑦 = cos3𝑥 . cot 4𝑥 9. 𝑦 = sin 5𝑥 cos 7𝑥 10. 𝑦 = cos 6𝑥 tan 2𝑥 Jawab: 1. 𝑦′ = 7𝑥6 + 30𝑥4 + 36𝑥2 2. 𝑦′ = −5𝑥−6 −6𝑥−4 −21𝑥−8 3. 𝑦 = 𝑥 2 2 + 𝑥 7 3 = 𝑥 + 𝑥 7 3 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 = 2𝑥 − 1 2 + 6𝑥 − 3 2 𝑦′ = 2. − 1 2 . 𝑥 − 1 2 − 2 2 + 6. − 3 2 . 𝑥 − 3 2 − 2 2 = −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′ = 2𝑥. sin 2𝑥 + 𝑥2 .2. cos 𝑥 𝑦′ = 2𝑥. sin2𝑥 + 2𝑥2 . cos 𝑥 6. 𝑢 = 𝑥2 + 1 → 𝑢′ = 2𝑥 𝑣 = cos3𝑥 → 𝑣′ = −3. sin 3𝑥 𝑦′ = 𝑢′ . 𝑣 + 𝑢. 𝑣′ = 2𝑥. cos3𝑥 + ( 𝑥2 + 1). −3. sin 3𝑥 𝑦′ = 2𝑥. cos3𝑥 + (−3𝑥2 − 3).sin 3𝑥 7. 𝑢 = sin 5𝑥 → 𝑢′ = 5. cos5𝑥 𝑣 = tan 2𝑥 → 𝑣′ = 2. 𝑠𝑒𝑐2 2𝑥 𝑦′ = 𝑢′ . 𝑣 + 𝑢. 𝑣′ = 5. cos5𝑥 . tan2𝑥 + sin 5𝑥 . 2. 𝑠𝑒𝑐2 2𝑥 𝑦′ = 5. cos5𝑥 .tan 2𝑥 + 2. sin 5𝑥 . 𝑠𝑒𝑐2 2𝑥 8. 𝑢 = cos3𝑥 → 𝑢′ = −3.sin 3𝑥 𝑣 = cot4𝑥 → 𝑣′ = −4. 𝑐𝑠𝑐2 4𝑥 𝑦′ = 𝑢′ . 𝑣 + 𝑢. 𝑣′ = −3. sin 3𝑥 . cot 4𝑥 + cos3𝑥 . −4. 𝑐𝑠𝑐2 4𝑥 𝑦′ = −3. sin 3𝑥 . cot 4𝑥 − 4. cos3𝑥 . 𝑐𝑠𝑐2 4𝑥 9. 𝑢 = sin 5𝑥 → 𝑢′ = 5. cos5𝑥 𝑣 = cos7𝑥 → 𝑣′ = −7. sin 7𝑥
2.
𝑦′ = 𝑢′ . 𝑣 −
𝑢. 𝑣′ 𝑣2 = 5. cos5𝑥 . cos7𝑥 − sin 5𝑥 . −7. sin 7𝑥 (cos7𝑥)2 𝑦′ = 5. cos5𝑥 .cos 7𝑥 + 7. sin 5𝑥 . sin 7𝑥 𝑐𝑜𝑠27𝑥 10. 𝑢 = cos6𝑥 → 𝑢′ = −6.sin 6𝑥 𝑣 = tan 2𝑥 → 𝑣′ = 2. 𝑠𝑒𝑐2 2𝑥 𝑦′ = 𝑢′ . 𝑣 − 𝑢. 𝑣′ 𝑣2 = −6. sin 6𝑥. tan 2𝑥 − cos6𝑥.2. 𝑠𝑒𝑐2 2𝑥 (tan 2𝑥)2 𝑦′ = −6. sin 6𝑥. tan2𝑥 − 2. cos6𝑥. 𝑠𝑒𝑐2 2𝑥 𝑡𝑎𝑛2 2𝑥
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