积分号下的求导公式 B() g(t; r)dr g(t; r)dr+g[t; B(tI aB(1) gt; a(t)) da(t) a(t dt=0 齐次方程a(c)=2cxkx+9(x)-= vu, (x t; r)dr t+(x v, (x, t; r)dr+f(r, t) f(x,) a Ddr+f(, t) Odt+ =f(x)积分号下的求导公式： t t g t t t t g t d g t t t g t d dt d t t t t   −   +   =   ( ) [ ; ( )] ( ) ( ; ) ( ; ) [ ; ( )] ( ) ( ) ( ) ( )             ( , ) ( , ; ) ( , ; ) ( , ; ) 0 0 v x t d v x t d v x t t t u x t t t t t = +   =       ( , ; ) . 0  = t vt x t  d 0 0 0 0 =0 = = + =   u t t vt t  d II 齐次方程 ( , ) ( , ; ) ( , ; ) 0 v x t d v x t t t u x t t t tt t +   =    ( , ; ) ( , ; ) 0 v x t d v x t t t t = tt +    ( ) ( , ) 0 2 2 u a u v a v d f x t t xx II tt xx II tt II − = − +   ( , ; ) ( , ) 0 v x t d f x t t = tt +    0 ( , ) 0 d f x t t = +   = f (x,t) ( ( , )) 0 v f x t t t= + =