erweitern (4(x+tan(x))^3)× (1+sec^2(x))

Lösung

erweitern

(4 (x + tan (x))^{3}) \cdot (1 + sec^{2} (x))

4 x^{3} + 12 x^{2} tan (x) + 12 x tan^{2} (x) + 4 tan^{3} (x) + 4 sec^{2} (x) x^{3} + 12 sec^{2} (x) x^{2} tan (x) + 12 x sec^{2} (x) tan^{2} (x) + 4 sec^{2} (x) tan^{3} (x)

Schritte zur Lösung

(4 (x + tan (x))^{3}) (1 + sec^{2} (x))

Wende das Distributivgesetz an:

a (b + c) = ab + a c

(4 (x + tan (x))^{3}) (1 + sec^{2} (x)) = 4 (x + tan (x))^{3} \cdot 1 + 4 (x + tan (x))^{3} sec^{2} (x)

= 4 (x + tan (x))^{3} \cdot 1 + 4 (x + tan (x))^{3} sec^{2} (x)

Vereinfache

4 (x + tan (x))^{3} \cdot 1 + 4 (x + tan (x))^{3} sec^{2} (x) : 4 (x + tan (x))^{3} + 4 sec^{2} (x) (x + tan (x))^{3}

= 4 (x + tan (x))^{3} + 4 sec^{2} (x) (x + tan (x))^{3}

Schreibe

4 (x + tan (x))^{3}

um:

4 x^{3} + 12 x^{2} tan (x) + 12 x tan^{2} (x) + 4 tan^{3} (x)

= 4 x^{3} + 12 x^{2} tan (x) + 12 x tan^{2} (x) + 4 tan^{3} (x) + 4 sec^{2} (x) (x + tan (x))^{3}

Schreibe

4 sec^{2} (x) (x + tan (x))^{3}

um:

4 sec^{2} (x) x^{3} + 12 sec^{2} (x) x^{2} tan (x) + 12 x sec^{2} (x) tan^{2} (x) + 4 sec^{2} (x) tan^{3} (x)

= 4 x^{3} + 12 x^{2} tan (x) + 12 x tan^{2} (x) + 4 tan^{3} (x) + 4 sec^{2} (x) x^{3} + 12 sec^{2} (x) x^{2} tan (x) + 12 x sec^{2} (x) tan^{2} (x) + 4 sec^{2} (x) tan^{3} (x)

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