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人気のある微分積分 >

derivative 3/(sin(x)+cos(x))

解

導関数

\frac{3}{sin ( x ) + cos ( x )}

解

- \frac{3 ( cos ( x ) - sin ( x ) )}{1 + sin ( 2 x )}

解答ステップ

\frac{d}{d x} (\frac{3}{sin ( x ) + cos ( x )})

定数を除去:

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

= 3 \frac{d}{d x} (\frac{1}{sin ( x ) + cos ( x )})

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

= 3 \frac{d}{d x} ((sin (x) + cos (x))^{- 1})

連鎖法則を適用:

- \frac{1}{( sin ( x ) + cos ( x ) ) ^{2}} \frac{d}{d x} (sin (x) + cos (x))

= - \frac{1}{( sin ( x ) + cos ( x ) ) ^{2}} \frac{d}{d x} (sin (x) + cos (x))

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

= 3 (- \frac{1}{( sin ( x ) + cos ( x ) ) ^{2}} (cos (x) - sin (x)))

簡素化

3 (- \frac{1}{( sin ( x ) + cos ( x ) ) ^{2}} (cos (x) - sin (x))) : - \frac{3 ( cos ( x ) - sin ( x ) )}{1 + sin ( 2 x )}

= - \frac{3 ( cos ( x ) - sin ( x ) )}{1 + sin ( 2 x )}

グラフ

人気の例

sum from i=1 to infinity of i^4

i = 1 \sum \infty i^{4}

(\partial)/(\partial x)(3x^4+8x^3)

\frac{\partial}{\partial x} (3 x^{4} + 8 x^{3})

d/(d{z)}((1-{y}){z})

\frac{d}{d z} ((1 - y) z)

\frac{d y}{d x} = 3 y

(\partial)/(\partial y)(5x^2)

\frac{\partial}{\partial y} (5 x^{2})