d/(da)(1+cos^4(a)-sin^4(a))

Lösung

\frac{d}{d a} (1 + cos^{4} (a) - sin^{4} (a))

- 4 cos (a) sin (a)

Schritte zur Lösung

\frac{d}{d a} (1 + cos^{4} (a) - sin^{4} (a))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d a} (1) + \frac{d}{d a} (cos^{4} (a)) - \frac{d}{d a} (sin^{4} (a))

\frac{d}{d a} (1) = 0

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

\frac{d}{d a} (sin^{4} (a)) = 4 sin^{3} (a) cos (a)

= 0 - 4 cos^{3} (a) sin (a) - 4 sin^{3} (a) cos (a)

Vereinfache

0 - 4 cos^{3} (a) sin (a) - 4 sin^{3} (a) cos (a) : - 4 cos (a) sin (a)

= - 4 cos (a) sin (a)

x \to \infty lim (\frac{2 x}{x})

im pl i c i t \frac{d y}{d x}, y = x^{3} + 2

x \to \infty lim (e^{0})

\frac{d}{d x} (9 x^{2} + 6 x - 2)

x \to 1 lim (\frac{x + 2}{1 - x})