derivative-2xsin(x^2)

Lösung

ableitung von

- 2 x sin (x^{2})

- 2 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sin (x^{2})

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

\frac{d x}{d x} = 1

\frac{d}{d x} (sin (x^{2})) = cos (x^{2}) \cdot 2 x

= - 2 (1 \cdot sin (x^{2}) + cos (x^{2}) \cdot 2 xx)

Vereinfache

- 2 (1 \cdot sin (x^{2}) + cos (x^{2}) \cdot 2 xx) : - 2 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

= - 2 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

\frac{d}{d x} (arcsin^{4} (x^{7} y^{2} + \frac{z}{x ^{3}}))

f^{^{''}} (x) = x^{3}

\int \frac{x}{y + x ^{2}} d x

7 x y \frac{d y}{d x} = 4

\int \frac{2 x + 1}{x - 1} d x