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人気のある微分積分 >

derivative of x(1-cos(x))

解

\frac{d}{d x} (x (1 - cos (x)))

解

1 - cos (x) + x sin (x)

解答ステップ

\frac{d}{d x} (x (1 - cos (x)))

積の法則を適用:

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

f = x, g = 1 - cos (x)

= \frac{d x}{d x} (1 - cos (x)) + \frac{d}{d x} (1 - cos (x)) x

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

\frac{d}{d x} (1 - cos (x)) = sin (x)

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

簡素化

= 1 - cos (x) + x sin (x)

グラフ

人気の例

integral from 0 to 2 of (4x^3-3x^2+2x)

\int_{0}^{2} (4 x^{3} - 3 x^{2} + 2 x) d x

integral of 1/5 e^{(-y)/5}

\int \frac{1}{5} e^{\frac{- y}{5}} d y

integral of (ln(y^2))/(3y)

\int \frac{ln ( y ^{2} )}{3 y} d y

tangent y=(10x)/(x^2-6),(4,4)

t an g e n t y = \frac{10 x}{x ^{2} - 6}, (4, 4)

limit as x approaches 1 of (ln(x))/(x-1)

x \to 1 lim (\frac{ln ( x )}{x - 1})