derivative of 4arccos(-5x)

解答

\frac{d}{d x} (4 arccos (- 5 x))

\frac{20}{1 - 25 x ^{2}}

求解步骤

\frac{d}{d x} (4 arccos (- 5 x))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (arccos (- 5 x))

使用连锁律:

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

= - \frac{1}{1 - ( - 5 x ) ^{2}} \frac{d}{d x} (- 5 x)

\frac{d}{d x} (- 5 x) = - 5

= 4 - \frac{1}{1 - ( - 5 x ) ^{2}} (- 5)

化简

4 - \frac{1}{1 - ( - 5 x ) ^{2}} (- 5) : \frac{20}{1 - 25 x ^{2}}

= \frac{20}{1 - 25 x ^{2}}

\frac{d}{d x} ((sin (x))^{4} + sin (x^{4}))

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