derivative of-sin(2/(x+1-e^{x^2}*2x))

解答

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

- \frac{cos ( \frac{2}{x + 1} - 2 e ^{x^{2}} x ) ( - 2 - 4 e ^{x^{2}} x ^{4} - 8 e ^{x^{2}} x ^{3} - 6 e ^{x^{2}} x ^{2} - 4 e ^{x^{2}} x - 2 e ^{x^{2}} )}{( x + 1 ) ^{2}}

求解步骤

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

将常数提出:

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

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

使用连锁律:

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

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

\frac{d}{d x} (\frac{2}{x + 1} - e^{x^{2}} \cdot 2 x) = \frac{- 2 - 4 e ^{x^{2}} x ^{4} - 8 e ^{x^{2}} x ^{3} - 6 e ^{x^{2}} x ^{2} - 4 e ^{x^{2}} x - 2 e ^{x^{2}}}{( x + 1 ) ^{2}}

= - cos (\frac{2}{x + 1} - e^{x^{2}} \cdot 2 x) \frac{- 2 - 4 e ^{x^{2}} x ^{4} - 8 e ^{x^{2}} x ^{3} - 6 e ^{x^{2}} x ^{2} - 4 e ^{x^{2}} x - 2 e ^{x^{2}}}{( x + 1 ) ^{2}}

分式相乘:

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

= - \frac{cos ( \frac{2}{x + 1} - 2 e ^{x^{2}} x ) ( - 2 - 4 e ^{x^{2}} x ^{4} - 8 e ^{x^{2}} x ^{3} - 6 e ^{x^{2}} x ^{2} - 4 e ^{x^{2}} x - 2 e ^{x^{2}} )}{( x + 1 ) ^{2}}