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人気のある微分積分 >

derivative xcos(3x)

解

導関数

x cos (3 x)

解

cos (3 x) - 3 x sin (3 x)

解答ステップ

\frac{d}{d x} (x cos (3 x))

積の法則を適用:

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

f = x, g = cos (3 x)

= \frac{d x}{d x} cos (3 x) + \frac{d}{d x} (cos (3 x)) x

\frac{d x}{d x} = 1

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= 1 \cdot cos (3 x) + (- sin (3 x) \cdot 3) x

簡素化

= cos (3 x) - 3 x sin (3 x)

グラフ

人気の例

derivative of 2sin(x-3cos(x))

\frac{d}{d x} (2 sin (x) - 3 cos (x))

derivative y=sqrt(4+3x)

d er i v a t i v e y = 4 + 3 x

limit as x approaches 25 of 2x+2sqrt(x)

x \to 25 lim (2 x + 2 x)

limit as x approaches 3 of (x-1)/(x^2-2)

x \to 3 lim (\frac{x - 1}{x ^{2} - 2})

x y^{2} d x = d y - x d x