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

Lösung

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

- 4 cos (a) sin (a) cos (2 a)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

4 sin^{3} (a) cos (a) - 4 cos^{3} (a) sin (a) : - 4 cos (a) sin (a) cos (2 a)

= - 4 cos (a) sin (a) cos (2 a)

\int \frac{sec ( x ) tan ( x )}{- 5 + sec ( x )} d x

x \to 0 + lim (9 cos (9 x))

\int \frac{e ^{x}}{e ^{x} - 2} d x

x \to 0 lim (- 4 x^{- 3})

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