derivative of arctan(sin(8x))

解答

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

\frac{8 cos ( 8 x )}{sin ^{2} ( 8 x ) + 1}

求解步骤

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

使用连锁律:

\frac{1}{( sin ( 8 x ) ) ^{2} + 1} \frac{d}{d x} (sin (8 x))

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

\frac{d}{d x} (sin (8 x)) = cos (8 x) \cdot 8

= \frac{1}{( sin ( 8 x ) ) ^{2} + 1} cos (8 x) \cdot 8

化简

\frac{1}{sin ^{2} ( 8 x ) + 1} cos (8 x) \cdot 8 : \frac{8 cos ( 8 x )}{sin ^{2} ( 8 x ) + 1}

= \frac{8 cos ( 8 x )}{sin ^{2} ( 8 x ) + 1}

t an g e n t f (x) = 2 - x e^{x}, at x = 0

y^{^{'}} = e^{- y} (2 x - 4), y (0) = 1

y^{^{''}} + 6 y^{^{'}} + 9 y = 4 e^{- 3 t}

y = ln (x^{3} e^{2 x})

d er i v a t i v e \frac{x ^{3} + 2}{3}