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

Lösung

\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}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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}}

Multipliziere Brüche:

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}}

in v erse l a pl a ce {\frac{3 !}{s ^{4} ( s + 2 ) ^{2}}}

d er i v a t i v e θ tan (θ)

\int \frac{2 x ^{3} - x ^{2} + 2 x + 4}{x ^{2} + 1} d x

\int e^{20 x} d x

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