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受欢迎的微积分 >

derivative f(x)=cos(2x)sin(5*x)

解答

导数

f (x) = cos (2 \cdot x) \cdot sin (5 \cdot x)

解答

- 2 sin (2 x) sin (5 x) + 5 cos (5 x) cos (2 x)

求解步骤

\frac{d}{d x} (cos (2 x) sin (5 x))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (2 x), g = sin (5 x)

= \frac{d}{d x} (cos (2 x)) sin (5 x) + \frac{d}{d x} (sin (5 x)) cos (2 x)

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= (- sin (2 x) \cdot 2) sin (5 x) + cos (5 x) \cdot 5 cos (2 x)

化简

= - 2 sin (2 x) sin (5 x) + 5 cos (5 x) cos (2 x)

作图

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