derivative of cos^4(x+sin^4(x))

Lösung

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

- 4 cos (x) sin (x) cos (2 x)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

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

x \to 3 + lim (\frac{3}{x - 3})

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

\frac{d}{d x} (cos (x^{2} e^{x}))

x \to - 2 lim (- x^{2} + 5 x - 1)

in v erse l a pl a ce F (s) = \frac{s ^{2} - 2 s - 6}{s - 2}