derivative arccos(x^2+3/2 x)

解答

导数

arccos (x^{2} + \frac{3}{2} x)

- \frac{4 x + 3}{4 - 4 x ^{4} - 12 x ^{3} - 9 x ^{2}}

求解步骤

\frac{d}{d x} (arccos (x^{2} + \frac{3}{2} x))

化简

arccos (x^{2} + \frac{3}{2} x) : arccos (x^{2} + \frac{3 x}{2})

= \frac{d}{d x} (arccos (x^{2} + \frac{3 x}{2}))

使用连锁律:

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

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

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

= - \frac{1}{1 - ( x ^{2} + \frac{3 x}{2} ) ^{2}} (2 x + \frac{3}{2})

化简

- \frac{1}{1 - ( x ^{2} + \frac{3 x}{2} ) ^{2}} (2 x + \frac{3}{2}) : - \frac{4 x + 3}{4 - 4 x ^{4} - 12 x ^{3} - 9 x ^{2}}

= - \frac{4 x + 3}{4 - 4 x ^{4} - 12 x ^{3} - 9 x ^{2}}

\frac{d}{d x} (e^{- 8 x} cos (8 x))

n = 0 \sum \infty e^{- n - 1}

\frac{\partial}{\partial y} (8 x^{2} + 7 y^{2} + 2)

\frac{d}{d x} (x (4^{- 2 x}))

\frac{d}{d x} (3 tan (5 x))