derivative of arccos(x/b)

解答

\frac{d}{d x} (arccos (\frac{x}{b}))

- \frac{1}{b ^{2} - x ^{2}}

求解步骤

\frac{d}{d x} (arccos (\frac{x}{b}))

使用连锁律:

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

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

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

= - \frac{1}{1 - ( \frac{x}{b} ) ^{2}} \cdot \frac{1}{b}

化简

- \frac{1}{1 - ( \frac{x}{b} ) ^{2}} \cdot \frac{1}{b} : - \frac{1}{b ^{2} - x ^{2}}

= - \frac{1}{b ^{2} - x ^{2}}

\frac{d ^{4}}{d x ^{4}} (\frac{8 x}{1 - x})

d er i v a t i v e f (x) = 5^{5 x + 1} + 3^{1 - 3 x}

y^{^{'}} + 5 y = 7

\frac{d ^{2}}{d x ^{2}} (- 2 x^{4} - 2 x^{3} + 60 x^{2} - 22)

\frac{d}{d x} (2 x cos (x) - 2 sin (x))