derivative of tan^4(cot(3x^4+5x))

解

\frac{d}{d x} (tan^{4} (cot (3 x^{4} + 5 x)))

- 4 tan^{3} (cot (3 x^{4} + 5 x)) sec^{2} (cot (3 x^{4} + 5 x)) csc^{2} (3 x^{4} + 5 x) (12 x^{3} + 5)

解答ステップ

\frac{d}{d x} (tan^{4} (cot (3 x^{4} + 5 x)))

連鎖法則を適用:

4 (tan (cot (3 x^{4} + 5 x)))^{3} \frac{d}{d x} (tan (cot (3 x^{4} + 5 x)))

= 4 (tan (cot (3 x^{4} + 5 x)))^{3} \frac{d}{d x} (tan (cot (3 x^{4} + 5 x)))

\frac{d}{d x} (tan (cot (3 x^{4} + 5 x))) = - sec^{2} (cot (3 x^{4} + 5 x)) csc^{2} (3 x^{4} + 5 x) (12 x^{3} + 5)

= 4 (tan (cot (3 x^{4} + 5 x)))^{3} (- sec^{2} (cot (3 x^{4} + 5 x)) csc^{2} (3 x^{4} + 5 x) (12 x^{3} + 5))

簡素化

= - 4 tan^{3} (cot (3 x^{4} + 5 x)) sec^{2} (cot (3 x^{4} + 5 x)) csc^{2} (3 x^{4} + 5 x) (12 x^{3} + 5)