erweitern (d^2)/(d^2x)(xy+5e^y=5e)

Lösung

erweitern

\frac{d ^{2}}{d ^{2} x} (x y + 5 e^{y} = 5 e)

y + \frac{5 e ^{y}}{x} = 13.59140 \dots

Schritte zur Lösung

\frac{d ^{2}}{d ^{2} x} (x y + 5 e^{y} = 5 e)

= \frac{d ^{2}}{d ^{2} x} (x y + 5 \cdot 5 e = e^{y})

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = \frac{d ^{2}}{d ^{2} x}, b = x y, c = 5 e^{y} = 5 e

\frac{d ^{2}}{d ^{2} x} x y + \frac{d ^{2}}{d ^{2} x} \cdot 5 e^{y} = 5 e

\frac{d ^{2}}{d ^{2} x} x y + 5 e^{y} \frac{d ^{2}}{d ^{2} x} = 5 e

Vereinfache

\frac{d ^{2}}{d ^{2} x} x y + 5 e^{y} \frac{d ^{2}}{d ^{2} x} = 5 e : y + \frac{5 e ^{y}}{x} = 13.59140 \dots

y + \frac{5 e ^{y}}{x} = 13.59140 \dots

e x p an d \frac{4.5805 ( z - 0.4776 )}{( z )}

s im pl i f y 40 (2 - 2)

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

s im pl i f y (\frac{x}{3} + \frac{1}{6}) (\frac{1}{6} + \frac{2 y}{3})

e x p an d m u lt i pl y (x^{2} + 0 x + 13) \cdot (x)