derivative f(x)=(arctan(8x))^2

解答

导数

f (x) = (arctan (8 x))^{2}

\frac{16 arctan ( 8 x )}{64 x ^{2} + 1}

求解步骤

\frac{d}{d x} ((arctan (8 x))^{2})

使用连锁律:

2 arctan (8 x) \frac{d}{d x} (arctan (8 x))

= 2 arctan (8 x) \frac{d}{d x} (arctan (8 x))

\frac{d}{d x} (arctan (8 x)) = \frac{8}{64 x ^{2} + 1}

= 2 arctan (8 x) \frac{8}{64 x ^{2} + 1}

化简

2 arctan (8 x) \frac{8}{64 x ^{2} + 1} : \frac{16 arctan ( 8 x )}{64 x ^{2} + 1}

= \frac{16 arctan ( 8 x )}{64 x ^{2} + 1}

e^{5 y} y^{^{'}} = x^{3}

\int (5 x + 1)^{19} d x

x \to 2 + lim (\frac{x}{2 - x})

t an g e n t y = e^{4 x}

y^{^{''}} + y^{^{'}} = \frac{1}{4} cos (3 t)