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人気のある微分積分 >

derivative t^8cos(t)

解

導関数

t^{8} cos (t)

解

8 t^{7} cos (t) - t^{8} sin (t)

解答ステップ

\frac{d}{d t} (t^{8} cos (t))

積の法則を適用:

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

f = t^{8}, g = cos (t)

= \frac{d}{d t} (t^{8}) cos (t) + \frac{d}{d t} (cos (t)) t^{8}

\frac{d}{d t} (t^{8}) = 8 t^{7}

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

= 8 t^{7} cos (t) + (- sin (t)) t^{8}

簡素化

= 8 t^{7} cos (t) - t^{8} sin (t)

グラフ

人気の例

laplacetransform t^2*e^{-,\at}

l a pl a ce t r an s f or m t^{2} \cdot e^{-, at}

tangent f(x)=x(4-x)^3,\at x=2

t an g e n t f (x) = x (4 - x)^{3}, at x = 2

laplacetransform f(t)=3sin(4t)-2e^{2t}

l a pl a ce t r an s f or m f (t) = 3 sin (4 t) - 2 e^{2 t}

derivative of sqrt(144-x)

\frac{d}{d x} (144 - x)

integral of (5-x^3)^4x^2

\int (5 - x^{3})^{4} x^{2} d x