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人気のある微分積分 >

derivative of sin^5(4x+1)

解

\frac{d}{d x} (sin^{5} (4 x + 1))

解

20 sin^{4} (4 x + 1) cos (4 x + 1)

解答ステップ

\frac{d}{d x} (sin^{5} (4 x + 1))

連鎖法則を適用:

5 (sin (4 x + 1))^{4} \frac{d}{d x} (sin (4 x + 1))

= 5 (sin (4 x + 1))^{4} \frac{d}{d x} (sin (4 x + 1))

\frac{d}{d x} (sin (4 x + 1)) = cos (4 x + 1) \cdot 4

= 5 (sin (4 x + 1))^{4} cos (4 x + 1) \cdot 4

簡素化

= 20 sin^{4} (4 x + 1) cos (4 x + 1)

グラフ

人気の例

y^'*(x^2+2)+4x(y^2+2y+1)=0

y^{^{'}} \cdot (x^{2} + 2) + 4 x (y^{2} + 2 y + 1) = 0

integral of (19)/(x^3-125)

\int \frac{19}{x ^{3} - 125} d x

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\int \frac{t ^{3}}{t ^{4} + 1} d t