derivative of 80picos(10pix)

解答

\frac{d}{d x} (80 π cos (10 π x))

- 800 π^{2} sin (10 π x)

求解步骤

\frac{d}{d x} (80 π cos (10 π x))

将常数提出:

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

= 80 π \frac{d}{d x} (cos (10 π x))

使用连锁律:

- sin (10 π x) \frac{d}{d x} (10 π x)

= - sin (10 π x) \frac{d}{d x} (10 π x)

\frac{d}{d x} (10 π x) = 10 π

= 80 π (- sin (10 π x) \cdot 10 π)

化简

80 π (- sin (10 π x) \cdot 10 π) : - 800 π^{2} sin (10 π x)

= - 800 π^{2} sin (10 π x)

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