derivative of-2sin(xcos(x)at[0.2pi])

解答

\frac{d}{d x} (- 2 sin (x) cos (x) a t [0.2 π])

- 1.25663 \dots a t cos (2 x)

求解步骤

\frac{d}{d x} (- 2 sin (x) cos (x) a t (0.2 π))

化简

- 2 sin (x) cos (x) a t (0.2 π) : - 1.25663 \dots a t sin (x) cos (x)

= \frac{d}{d x} (- 1.25663 \dots a t sin (x) cos (x))

将

a, t

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= - 1.25663 \dots a t \frac{d}{d x} (sin (x) cos (x))

使用微分乘法定则:

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

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

= - 1.25663 \dots a t (\frac{d}{d x} (sin (x)) cos (x) + \frac{d}{d x} (cos (x)) sin (x))

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

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

= - 1.25663 \dots a t (cos (x) cos (x) + (- sin (x)) sin (x))

化简

- 1.25663 \dots a t (cos (x) cos (x) + (- sin (x)) sin (x)) : - 1.25663 \dots a t cos (2 x)

= - 1.25663 \dots a t cos (2 x)

in v erse l a pl a ce \frac{18}{( s + 1 ) ^{2} ( s ^{2} + 4 )}

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