Question

【数学】求导题已知函数y=y(x)由方程 2^(x*y) = x + y 确定,求dy|x=0注意是2的x乘以y次方~

Answer 1

2^(xy) = x + y,当x=0时,y = 1

(xy)ln2 = ln(x+y)

两边微分得：

(ydx + xdy)ln2 = (dx+dy)(x+y)

代入x=0,y=1 得

ln2dx = dx+dy

所以,dy = (ln2 - 1)dx