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人気のある微分積分 >

(\partial)/(\partial y)(y^6cos(5x))

解

\frac{\partial}{\partial y} (y^{6} cos (5 x))

解

6 y^{5} cos (5 x)

解答ステップ

\frac{\partial}{\partial y} (y^{6} cos (5 x))

x

を定数として扱う

定数を除去:

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

= cos (5 x) \frac{\partial}{\partial y} (y^{6})

乗の法則を適用:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= cos (5 x) \cdot 6 y^{6 - 1}

簡素化

= 6 y^{5} cos (5 x)

人気の例

integral from 1 to 2 of (7x-2)/(3x^2-2x)

\int_{1}^{2} \frac{7 x - 2}{3 x ^{2} - 2 x} d x

tangent f(x)=(4x+3)(-x+1),\at x=4

t an g e n t f (x) = (4 x + 3) (- x + 1), at x = 4

derivative of 6/(\sqrt[4]{x})

\frac{d}{d x} (\frac{6}{4 x})

tangent f(x)=7x-x^2,(1,6)

t an g e n t f (x) = 7 x - x^{2}, (1, 6)

integral from-1 to 1 of 1/x

\int_{- 1}^{1} \frac{1}{x} d x