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人気のある微分積分 >

derivative of asin^3(x)

解

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

解

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

解答ステップ

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

定数を除去:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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

グラフ

人気の例

limit as x approaches 0-of (14x^3+15x)/x

x \to 0 - lim (\frac{14 x ^{3} + 15 x}{x})

マクローリン ln(1/3 (2+e^{-3x}))

ma c l a u r in ln (\frac{1}{3} (2 + e^{- 3 x}))

y^{''}-4y+4y=e^{-t},y(0)=0,y^'(0)=0

y^{^{''}} - 4 y + 4 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 0

limit as x approaches+0 of 3^x+7

x \to + 0 lim (3^{x} + 7)

derivative ((t^3)/(t^8+9))^2

d er i v a t i v e (\frac{t ^{3}}{t ^{8} + 9})^{2}