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

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

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

\int \frac{1}{x ^{2} + x - 12} d x

d er i v a t i v e t e^{- t}

\frac{d}{d x} (\frac{2 x ^{5} + 3 x ^{4} - 1}{- 2 x ^{7}})

\frac{d}{d θ} (- cos (θ))

\int \frac{6}{2 x - 5} d x