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人気のある微分積分 >

derivative of sin(x(-2x))

解

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

解

- 2 x cos (x) - 2 sin (x)

解答ステップ

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

積の法則を適用:

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

f = sin (x), g = - 2 x

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

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

\frac{d}{d x} (- 2 x) = - 2

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

簡素化

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

グラフ

人気の例

derivative of (x^{6/7}/5)

\frac{d}{d x} (\frac{x ^{\frac{6}{7}}}{5})

derivative 1/(x^2+3x-1)

d er i v a t i v e \frac{1}{x ^{2} + 3 x - 1}

integral of 1/((x-1)^2+4)

\int \frac{1}{( x - 1 ) ^{2} + 4} d x

integral from 0 to pi of t*sin(3t)

\int_{0}^{π} t \cdot sin (3 t) d t

sum from n=0 to infinity of 2/(5^{n-1)}

n = 0 \sum \infty \frac{2}{5 ^{n - 1}}