derivative f(x)=csc^3(5x^2+1)

解

導関数

f (x) = csc^{3} (5 x^{2} + 1)

- 30 x csc^{3} (5 x^{2} + 1) cot (5 x^{2} + 1)

解答ステップ

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

連鎖法則を適用:

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

= 3 (csc (5 x^{2} + 1))^{2} \frac{d}{d x} (csc (5 x^{2} + 1))

\frac{d}{d x} (csc (5 x^{2} + 1)) = - cot (5 x^{2} + 1) csc (5 x^{2} + 1) \cdot 10 x

= 3 (csc (5 x^{2} + 1))^{2} (- cot (5 x^{2} + 1) csc (5 x^{2} + 1) \cdot 10 x)

簡素化

3 csc^{2} (5 x^{2} + 1) (- cot (5 x^{2} + 1) csc (5 x^{2} + 1) \cdot 10 x) : - 30 x csc^{3} (5 x^{2} + 1) cot (5 x^{2} + 1)

= - 30 x csc^{3} (5 x^{2} + 1) cot (5 x^{2} + 1)