erweitern f''(x)(x-1)(x-3)^2

Lösung

erweitern

f^{''} (x) (x - 1) (x - 3)^{2}

x^{3} f'' (x) - 7 x^{2} f'' (x) + 15 x f'' (x) - 9 f'' (x)

Schritte zur Lösung

f^{''} (x) (x - 1) (x - 3)^{2}

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = f^{''} (x) (x - 3)^{2}, b = x, c = 1

= f^{^{''}} (x) (x - 3)^{2} x - f^{^{''}} (x) (x - 3)^{2} \cdot 1

= x f^{^{''}} (x) (x - 3)^{2} - 1 f^{^{''}} (x) (x - 3)^{2}

Vereinfache

x f^{''} (x) (x - 3)^{2} - 1 f^{''} (x) (x - 3)^{2} : x^{3} f^{''} (x) - 7 x^{2} f^{''} (x) + 15 x f^{''} (x) - 9 f^{''} (x)

= x^{3} f^{''} (x) - 7 x^{2} f^{''} (x) + 15 x f^{''} (x) - 9 f^{''} (x)

e x p an d \frac{- 1 + 5 s}{3 s ( s - 1 ) ^{2}}

e x p an d (x^{2} - 4 x + 1) l e f t (- x^{3} + 2 x)

e x p an d lo g_{5} (27) + ln (32)

e x p an d e^{4 t} (- e^{- 2 t} - 2 t) + e^{2 t} (2 t + e^{2 t})

s im pl i f y 2 \cdot (cos (θ) + 2 sin (θ))