請問可否詳細 d 一次呢條數呢 ?

你可以使用Implicit Differentiation

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多謝!!

Let y = e^x
ln(y) = x
( d[ln(y]/dy )( dy/dx ) = dx/dx ... by chain rule
d[ln(y)]/dy = 1/(dy/dx) = 1/y
Therefore,
d[ln(x)]/dx = 1/x

For your question, w(x) is a function of x and y is not a function of x
let w = y^x
ln(w) = x ln(y)
d ln(w) /dx = d [x ln(y)] /dx
LHS = d ln(w) /dx
= ( d ln(w)/dw )( dw/dx ) ... by chain rule
= ( 1/w )( dw/dx)
RHS = d [x ln(y)] /dx
= (dx/dx) ln(y) ... as y is not a function of x, otherwise it is wrong.
= ln(y)
Combine LHS and RHS
( 1/w )( dw/dx) = ln(y)
dw/dx = (w)( ln(y) )
= y^x ( ln(y) )

Please be reminded that if y is a function of x, ie y(x), the solution will be different.