erweitern (8tan(x)+8cos(x)+8csc(x))^2

Lösung

erweitern

(8 tan (x) + 8 cos (x) + 8 csc (x))^{2}

64 cos^{2} (x) + 64 csc^{2} (x) + 64 tan^{2} (x) + 128 cot (x) + 128 sin (x) + 128 csc (x) tan (x)

Schritte zur Lösung

(8 tan (x) + 8 cos (x) + 8 csc (x))^{2}

Wende Exponentenregel an:

a^{b + c} = a^{b} \cdot a^{c}

(8 tan (x) + 8 cos (x) + 8 csc (x))^{2} = (8 tan (x) + 8 cos (x) + 8 csc (x)) (8 tan (x) + 8 cos (x) + 8 csc (x))

= (8 tan (x) + 8 cos (x) + 8 csc (x)) (8 tan (x) + 8 cos (x) + 8 csc (x))

Setze Klammern

= 8 tan (x) \cdot 8 tan (x) + 8 tan (x) \cdot 8 cos (x) + 8 tan (x) \cdot 8 csc (x) + 8 cos (x) \cdot 8 tan (x) + 8 cos (x) \cdot 8 cos (x) + 8 cos (x) \cdot 8 csc (x) + 8 csc (x) \cdot 8 tan (x) + 8 csc (x) \cdot 8 cos (x) + 8 csc (x) \cdot 8 csc (x)

Vereinfache

8 tan (x) \cdot 8 tan (x) + 8 tan (x) \cdot 8 cos (x) + 8 tan (x) \cdot 8 csc (x) + 8 cos (x) \cdot 8 tan (x) + 8 cos (x) \cdot 8 cos (x) + 8 cos (x) \cdot 8 csc (x) + 8 csc (x) \cdot 8 tan (x) + 8 csc (x) \cdot 8 cos (x) + 8 csc (x) \cdot 8 csc (x) : 64 cos^{2} (x) + 64 csc^{2} (x) + 64 tan^{2} (x) + 128 cot (x) + 128 sin (x) + 128 csc (x) tan (x)

= 64 cos^{2} (x) + 64 csc^{2} (x) + 64 tan^{2} (x) + 128 cot (x) + 128 sin (x) + 128 csc (x) tan (x)

e x p an d x \cdot (8 - 2 ln (x))

e x p an d \frac{( ( 1 - cos ( x ) ) ^{2} + sin ^{2} ( x ) )}{1 - cos ( x )}

e x p an d \frac{3 x + 4}{( x + 4 ) ( x ^{2} + x - 4 ) ^{2}}

s im pl i f y (3 1 + x - 1) \cdot (1 + x + 1)

\frac{d}{d y} ((M) (2 x + y))