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Beliebt Rechnen >

d/(dt)(cos^4(t)-sin^4(t))

Lösung

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

Lösung

- sin (2 t) \cdot 2

Schritte zur Lösung

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

Vereinfache

cos^{4} (t) - sin^{4} (t) : cos (2 t)

= \frac{d}{d t} (cos (2 t))

Wende die Kettenregel an:

- sin (2 t) \frac{d}{d t} (2 t)

= - sin (2 t) \frac{d}{d t} (2 t)

\frac{d}{d t} (2 t) = 2

= - sin (2 t) \cdot 2

Graph

Beliebte Beispiele

derivative y=-x^3(3x^4-2)

d er i v a t i v e y = - x^{3} (3 x^{4} - 2)

derivative (f^{-1})(d)

d er i v a t i v e (f^{- 1}) (d)

derivative (3/2)^x

d er i v a t i v e (\frac{3}{2})^{x}

derivative (x^2)/(sqrt(4-x^2))

d er i v a t i v e \frac{x ^{2}}{4 - x ^{2}}

d/(da)(1+6cos^2(a)+cos^4(a))

\frac{d}{d a} (1 + 6 cos^{2} (a) + cos^{4} (a))