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人気のある微分積分 >

d/(dt)(3cos^6(t))

解

\frac{d}{d t} (3 cos^{6} (t))

解

- 18 cos^{5} (t) sin (t)

解答ステップ

\frac{d}{d t} (3 cos^{6} (t))

定数を除去:

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

= 3 \frac{d}{d t} (cos^{6} (t))

連鎖法則を適用:

6 (cos (t))^{5} \frac{d}{d t} (cos (t))

= 6 (cos (t))^{5} \frac{d}{d t} (cos (t))

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

= 3 \cdot 6 (cos (t))^{5} (- sin (t))

簡素化

= - 18 cos^{5} (t) sin (t)

グラフ

人気の例

derivative f(x)=((x^3+4x-1))/(x^2)

d er i v a t i v e f (x) = \frac{( x ^{3} + 4 x - 1 )}{x ^{2}}

derivative ((1+2x+x^2))/(e^x)

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

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

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

derivative 4xln(2x+1)

d er i v a t i v e 4 x ln (2 x + 1)

d/(dq)(2600-13q)

\frac{d}{d q} (2600 - 13 q)