derivative of cos(x^2-2x^2sin(x^2))

Lösung

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

- 6 x sin (x^{2}) - 4 x^{3} cos (x^{2})

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Vereinfache

- sin (x^{2}) \cdot 2 x - 2 (2 x sin (x^{2}) + 2 x^{3} cos (x^{2})) : - 6 x sin (x^{2}) - 4 x^{3} cos (x^{2})

= - 6 x sin (x^{2}) - 4 x^{3} cos (x^{2})

\frac{d}{d x} (1 - tan^{2} (x))

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

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

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

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