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人気のある微分積分 >

d/(dt)(asin^3(t))

解

\frac{d}{d t} (a sin^{3} (t))

解

3 a sin^{2} (t) cos (t)

解答ステップ

\frac{d}{d t} (a sin^{3} (t))

定数を除去:

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

= a \frac{d}{d t} (sin^{3} (t))

連鎖法則を適用:

3 (sin (t))^{2} \frac{d}{d t} (sin (t))

= 3 (sin (t))^{2} \frac{d}{d t} (sin (t))

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

= a \cdot 3 (sin (t))^{2} cos (t)

簡素化

= 3 a sin^{2} (t) cos (t)

グラフ

人気の例

(d^2)/(dx^2)(sqrt(x)-2/x)

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

(\partial)/(\partial y)(x^2-xy-y^2)

\frac{\partial}{\partial y} (x^{2} - x y - y^{2})

integral of (3x^3-sqrt(x))/x

\int \frac{3 x ^{3} - x}{x} d x

integral of \sqrt[3]{4-3x^2}(-6x)

\int 3 4 - 3 x^{2} (- 6 x) d x

derivative of |x^2-2x-3|

\frac{d}{d x} (x^{2} - 2 x - 3)