(\partial)/(\partial t)((x-ct)^4+(x+ct)^4)

פתרון

\frac{\partial}{\partial t} ((x - c t)^{4} + (x + c t)^{4})

8 c^{4} t^{3} + 24 c^{2} x^{2} t

צעדי פתרון

\frac{\partial}{\partial t} ((x - c t)^{4} + (x + c t)^{4})

(x - c t)^{4} + (x + c t)^{4}

פשט את:

2 x^{4} + 12 c^{2} x^{2} t^{2} + 2 c^{4} t^{4}

= \frac{\partial}{\partial t} (2 x^{4} + 12 c^{2} x^{2} t^{2} + 2 c^{4} t^{4})

כאל קבוע

c, x

התייחס ל

(f \pm g)^{'} = f^{'} \pm g^{'}

:השתמש בחוק החיבור

= \frac{\partial}{\partial t} (2 x^{4}) + \frac{\partial}{\partial t} (12 c^{2} x^{2} t^{2}) + \frac{\partial}{\partial t} (2 c^{4} t^{4})

\frac{\partial}{\partial t} (2 x^{4}) = 0

\frac{\partial}{\partial t} (12 c^{2} x^{2} t^{2}) = 24 c^{2} x^{2} t

\frac{\partial}{\partial t} (2 c^{4} t^{4}) = 8 c^{4} t^{3}

= 0 + 24 c^{2} x^{2} t + 8 c^{4} t^{3}

פשט

= 8 c^{4} t^{3} + 24 c^{2} x^{2} t