展开-0.1sin(10x+4t-pi/2)(10(dx)/(dt)+4)

解答

展开

- 0.1 sin (10 x + 4 t - \frac{π}{2}) (10 \frac{d x}{d t} + 4)

- sin (10 x + 4 t - \frac{π}{2}) \frac{d x}{d t} - 0.4 sin (10 x + 4 t - \frac{π}{2})

求解步骤

- 0.1 sin (10 x + 4 t - \frac{π}{2}) (10 \frac{d x}{d t} + 4)

使用分配律:

a (b + c) = ab + a c

a = - 0.1 sin (10 x + 4 t - \frac{π}{2}), b = 10 \frac{d x}{d t}, c = 4

= - 0.1 sin (10 x + 4 t - \frac{π}{2}) \cdot 10 \frac{d x}{d t} + (- 0.1 sin (10 x + 4 t - \frac{π}{2})) \cdot 4

使用加减运算法则

+ (- a) = - a

= - 10 \cdot 0.1 sin (10 x + 4 t - \frac{π}{2}) \frac{d x}{d t} - 4 \cdot 0.1 sin (10 x + 4 t - \frac{π}{2})

化简

- 10 \cdot 0.1 sin (10 x + 4 t - \frac{π}{2}) \frac{d x}{d t} - 4 \cdot 0.1 sin (10 x + 4 t - \frac{π}{2}) : - sin (10 x + 4 t - \frac{π}{2}) \frac{d x}{d t} - 0.4 sin (10 x + 4 t - \frac{π}{2})

= - sin (10 x + 4 t - \frac{π}{2}) \frac{d x}{d t} - 0.4 sin (10 x + 4 t - \frac{π}{2})

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