高数 多元复合函数的求导法则 偏导

Question

高数 多元复合函数的求导法则 偏导不知道这题怎么算

Answer 1

t^2=x^2+y^2

2t.∂t/∂x = 2x
∂t/∂x = x/t
2t.∂t/∂y = 2y
∂t/∂y = y/t
/
u=xln(x+t)-t
∂u/∂x
= [x/(x+t)] ( 1+ ∂t/∂x) + ln(x+t) - ∂t/∂x
= [x/(x+t)] ( 1+ (x/t)) + ln(x+t) - x/t
=x/t +ln(x+t) - x/t
=ln(x+t)
/
u=xln(x+t)-t
∂u/∂y
= [x/(x+t)] ( ∂t/∂y) - ∂t/∂y
= [x/(x+t)] (y/t) - y/t
=[xy- y(x+t) ]/[t(x+t)]
= -ty/[t(x+t)]
=-y/(x+t)
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