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人気のある微分積分 >

derivative of sin^{-3}(x)

解

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

解

- \frac{3 cos ( x )}{sin ^{4} ( x )}

解答ステップ

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

連鎖法則を適用:

- \frac{3}{( sin ( x ) ) ^{4}} \frac{d}{d x} (sin (x))

= - \frac{3}{( sin ( x ) ) ^{4}} \frac{d}{d x} (sin (x))

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

= - \frac{3}{( sin ( x ) ) ^{4}} cos (x)

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{3 cos ( x )}{sin ^{4} ( x )}

グラフ

人気の例

integral of ((x^5+x^2-x+5)/x)

\int (\frac{x ^{5} + x ^{2} - x + 5}{x}) d x

勾配 (2,-4),(5,8)

s l o p e (2, - 4), (5, 8)

(\partial)/(\partial y)(x^2-xy+9y^2)

\frac{\partial}{\partial y} (x^{2} - x y + 9 y^{2})

(\partial)/(\partial x)(9e^{sqrt(xy)})

\frac{\partial}{\partial x} (9 e^{x y})

derivative of (e^{sqrt(ln(x)})^{2^{-x}})

\frac{d}{d x} ((e^{l n (x)})^{2^{- x}})