derivative of 2cos(x^2-4x^2sin(x^2))

Lösung

\frac{d}{d x} (2 cos (x^{2}) - 4 x^{2} sin (x^{2}))

- 12 x sin (x^{2}) - 8 x^{3} cos (x^{2})

Schritte zur Lösung

\frac{d}{d x} (2 cos (x^{2}) - 4 x^{2} sin (x^{2}))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (2 cos (x^{2})) - \frac{d}{d x} (4 x^{2} sin (x^{2}))

\frac{d}{d x} (2 cos (x^{2})) = - 4 x sin (x^{2})

\frac{d}{d x} (4 x^{2} sin (x^{2})) = 4 (2 x sin (x^{2}) + 2 x^{3} cos (x^{2}))

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

Vereinfache

- 4 x sin (x^{2}) - 4 (2 x sin (x^{2}) + 2 x^{3} cos (x^{2})) : - 12 x sin (x^{2}) - 8 x^{3} cos (x^{2})

= - 12 x sin (x^{2}) - 8 x^{3} cos (x^{2})

in v erse l a pl a ce \frac{3}{s ( s ^{2} + 6 s )}

\int_{0}^{10} 400 - 20 t d t

d er i v a t i v e 16 e^{x}

s l o p e (3 - 1) (3 - 4)

\frac{d y}{d x} = 7 x + y - 7