d/(db)(sin^4(2b)-cos^4(2b))

解答

\frac{d}{d b} (sin^{4} (2 b) - cos^{4} (2 b))

8 cos (2 b) sin (2 b)

求解步骤

\frac{d}{d b} (sin^{4} (2 b) - cos^{4} (2 b))

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d b} (sin^{4} (2 b)) - \frac{d}{d b} (cos^{4} (2 b))

\frac{d}{d b} (sin^{4} (2 b)) = 8 sin^{3} (2 b) cos (2 b)

\frac{d}{d b} (cos^{4} (2 b)) = - 8 cos^{3} (2 b) sin (2 b)

= 8 sin^{3} (2 b) cos (2 b) - (- 8 cos^{3} (2 b) sin (2 b))

化简

8 sin^{3} (2 b) cos (2 b) - (- 8 cos^{3} (2 b) sin (2 b)) : 8 cos (2 b) sin (2 b)

= 8 cos (2 b) sin (2 b)

2 x^{2} y - x^{3} y^{^{'}} = y^{3}

\int \frac{x ^{2}}{1 + x ^{6}} d x

\int \frac{x ^{2}}{a} e^{- \frac{x}{a}} d x

\frac{\partial}{\partial x} (e^{(t - x)})

\frac{d}{d x} (4 x^{2} - 5)