erweitern x^{cos(x)}(-sin(x)ln(x)+(cos(x))/x)

Lösung

erweitern

x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

- x^{c o s (x)} sin (x) ln (x) + x^{c o s (x) - 1} cos (x)

Schritte zur Lösung

x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = x^{c o s (x)}, b = - sin (x) ln (x), c = \frac{cos ( x )}{x}

= x^{c o s (x)} (- sin (x) ln (x)) + x^{c o s (x)} \frac{cos ( x )}{x}

Wende Minus-Plus Regeln an

+ (- a) = - a

= - x^{c o s (x)} sin (x) ln (x) + \frac{cos ( x )}{x} x^{c o s (x)}

\frac{cos ( x )}{x} x^{c o s (x)} = x^{c o s (x) - 1} cos (x)

= - x^{c o s (x)} sin (x) ln (x) + x^{c o s (x) - 1} cos (x)

e x p an d \frac{- x ^{3} + 3 x ^{2} ( x + 2 ) - 1}{( x + 2 )}

e x p an d tan (θ) (cot (θ) + csc (θ))

e x p an d tan (\frac{x}{2}) + (1 - cos (x)) \cdot cot (x)

s im pl i f y (\frac{25 x ^{3}}{3} + 3750 x^{2} + 375000 x + 12500000) \cdot 20

e x p an d e^{7 - 43} (\frac{1}{2} + 23)