erweitern ((x+h)^2+1)(xln(x)+e^x)

Lösung

erweitern

((x + h)^{2} + 1) (x ln (x) + e^{x})

x^{3} ln (x) + 2 x^{2} h ln (x) + x h^{2} ln (x) + e^{x} x^{2} + 2 e^{x} x h + e^{x} h^{2} + x ln (x) + e^{x}

Schritte zur Lösung

((x + h)^{2} + 1) (x ln (x) + e^{x})

Wende Ausklammerungsregel an (VANI):

(a + b) (c + d) = a c + a d + b c + b d

a = (x + h)^{2}, b = 1, c = x ln (x), d = e^{x}

= (x + h)^{2} x ln (x) + (x + h)^{2} e^{x} + 1 \cdot x ln (x) + 1 \cdot e^{x}

= x ln (x) (x + h)^{2} + e^{x} (x + h)^{2} + 1 \cdot x ln (x) + 1 \cdot e^{x}

Vereinfache

x ln (x) (x + h)^{2} + e^{x} (x + h)^{2} + 1 \cdot x ln (x) + 1 \cdot e^{x} : x^{3} ln (x) + 2 x^{2} h ln (x) + x h^{2} ln (x) + e^{x} x^{2} + 2 e^{x} x h + e^{x} h^{2} + x ln (x) + e^{x}

= x^{3} ln (x) + 2 x^{2} h ln (x) + x h^{2} ln (x) + e^{x} x^{2} + 2 e^{x} x h + e^{x} h^{2} + x ln (x) + e^{x}

s im pl i f y 2 t (x) x^{^{''}} + (t (x) - 4) x^{^{'}} - x

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

e x p an d (w (x, y (x, z), z) + x^{^{'}} + y (x, z) z) (x + z)

e x p an d - 2 (2 - 3)

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