derivative of 2arcsin(x^4)

解答

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

\frac{8 x ^{3}}{1 - x ^{8}}

求解步骤

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

将常数提出:

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

= 2 \frac{d}{d x} (arcsin (x^{4}))

使用连锁律:

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

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

= 2 \cdot \frac{1}{1 - ( x ^{4} ) ^{2}} \cdot 4 x^{3}

化简

2 \cdot \frac{1}{1 - ( x ^{4} ) ^{2}} \cdot 4 x^{3} : \frac{8 x ^{3}}{1 - x ^{8}}

= \frac{8 x ^{3}}{1 - x ^{8}}

d er i v a t i v e sin (1)

\int \frac{x + 4}{x ^{2} + 4 x + 4} d x

\frac{\partial}{\partial y} (ln (x + y))

\frac{d y}{d x} = x x - 24

t an g e n t x^{2} + y^{2} = 29, (2, - 5)