derivative of 2csc(pi/4 x+1)

解

\frac{d}{d x} (2 csc (\frac{π}{4} x) + 1)

- \frac{π}{2} cot (\frac{π x}{4}) csc (\frac{π x}{4})

解答ステップ

\frac{d}{d x} (2 csc (\frac{π}{4} x) + 1)

簡素化

2 csc (\frac{π}{4} x) + 1 : 2 csc (\frac{π x}{4}) + 1

= \frac{d}{d x} (2 csc (\frac{π x}{4}) + 1)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 csc (\frac{π x}{4})) + \frac{d}{d x} (1)

\frac{d}{d x} (2 csc (\frac{π x}{4})) = - \frac{π}{2} cot (\frac{π x}{4}) csc (\frac{π x}{4})

\frac{d}{d x} (1) = 0

= - \frac{π}{2} cot (\frac{π x}{4}) csc (\frac{π x}{4}) + 0

簡素化

= - \frac{π}{2} cot (\frac{π x}{4}) csc (\frac{π x}{4})