확장 5(3x^2-4x+1)^4 derivative of 3x^2-4x+1

해법

확장

5 (3 x^{2} - 4 x + 1)^{4} \frac{d}{d x} (3 x^{2} - 4 x + 1)

405 x^{8} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 2160 x^{7} \frac{d}{d x} (3 x^{2} - 4 x + 1) + 4860 x^{6} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 6000 x^{5} \frac{d}{d x} (3 x^{2} - 4 x + 1) + 4430 x^{4} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 2000 x^{3} \frac{d}{d x} (3 x^{2} - 4 x + 1) + 540 x^{2} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 80 x \frac{d}{d x} (3 x^{2} - 4 x + 1) + 5 \frac{d}{d x} (3 x^{2} - 4 x + 1)

솔루션 단계

5 (3 x^{2} - 4 x + 1)^{4} \frac{d}{d x} (3 x^{2} - 4 x + 1)

(3 x^{2} - 4 x + 1)^{4} = 81 x^{8} - 432 x^{7} + 972 x^{6} - 1200 x^{5} + 886 x^{4} - 400 x^{3} + 108 x^{2} - 16 x + 1

= 5 (81 x^{8} - 432 x^{7} + 972 x^{6} - 1200 x^{5} + 886 x^{4} - 400 x^{3} + 108 x^{2} - 16 x + 1) \frac{d}{d x} (3 x^{2} - 4 x + 1)

괄호 배포

= 5 \frac{d}{d x} (3 x^{2} - 4 x + 1) 81 x^{8} + 5 \frac{d}{d x} (3 x^{2} - 4 x + 1) (- 432 x^{7}) + 5 \frac{d}{d x} (3 x^{2} - 4 x + 1) 972 x^{6} + 5 \frac{d}{d x} (3 x^{2} - 4 x + 1) (- 1200 x^{5}) + 5 \frac{d}{d x} (3 x^{2} - 4 x + 1) 886 x^{4} + 5 \frac{d}{d x} (3 x^{2} - 4 x + 1) (- 400 x^{3}) + 5 \frac{d}{d x} (3 x^{2} - 4 x + 1) 108 x^{2} + 5 \frac{d}{d x} (3 x^{2} - 4 x + 1) (- 16 x) + 5 \frac{d}{d x} (3 x^{2} - 4 x + 1) 1

마이너스 플러스 규칙 적용

+ (- a) = - a

= 5 \cdot 81 x^{8} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 5 \cdot 432 x^{7} \frac{d}{d x} (3 x^{2} - 4 x + 1) + 5 \cdot 972 x^{6} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 5 \cdot 1200 x^{5} \frac{d}{d x} (3 x^{2} - 4 x + 1) + 5 \cdot 886 x^{4} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 5 \cdot 400 x^{3} \frac{d}{d x} (3 x^{2} - 4 x + 1) + 5 \cdot 108 x^{2} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 5 \cdot 16 x \frac{d}{d x} (3 x^{2} - 4 x + 1) + 5 \cdot 1 \frac{d}{d x} (3 x^{2} - 4 x + 1)

5 \cdot 81 x^{8} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 5 \cdot 432 x^{7} \frac{d}{d x} (3 x^{2} - 4 x + 1) + 5 \cdot 972 x^{6} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 5 \cdot 1200 x^{5} \frac{d}{d x} (3 x^{2} - 4 x + 1) + 5 \cdot 886 x^{4} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 5 \cdot 400 x^{3} \frac{d}{d x} (3 x^{2} - 4 x + 1) + 5 \cdot 108 x^{2} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 5 \cdot 16 x \frac{d}{d x} (3 x^{2} - 4 x + 1) + 5 \cdot 1 \frac{d}{d x} (3 x^{2} - 4 x + 1)

단순화하세요:

405 x^{8} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 2160 x^{7} \frac{d}{d x} (3 x^{2} - 4 x + 1) + 4860 x^{6} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 6000 x^{5} \frac{d}{d x} (3 x^{2} - 4 x + 1) + 4430 x^{4} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 2000 x^{3} \frac{d}{d x} (3 x^{2} - 4 x + 1) + 540 x^{2} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 80 x \frac{d}{d x} (3 x^{2} - 4 x + 1) + 5 \frac{d}{d x} (3 x^{2} - 4 x + 1)

= 405 x^{8} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 2160 x^{7} \frac{d}{d x} (3 x^{2} - 4 x + 1) + 4860 x^{6} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 6000 x^{5} \frac{d}{d x} (3 x^{2} - 4 x + 1) + 4430 x^{4} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 2000 x^{3} \frac{d}{d x} (3 x^{2} - 4 x + 1) + 540 x^{2} \frac{d}{d x} (3 x^{2} - 4 x + 1) - 80 x \frac{d}{d x} (3 x^{2} - 4 x + 1) + 5 \frac{d}{d x} (3 x^{2} - 4 x + 1)