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用对数求导法求导数y={(x-5)/[(x^2+2)^(1/5)]}^(1/5)
题目详情
用对数求导法求导数
y={(x-5)/[(x^2+2)^(1/5)]}^(1/5)
y={(x-5)/[(x^2+2)^(1/5)]}^(1/5)
▼优质解答
答案和解析
ln|y|=(1/5)(ln|x-5|-(1/5)ln(x^2+2))
两边求导数得：
y'/y=(1/5)(1/(x-5)-(1/5)*2x/(x^2+2))
所以：y'={(x-5)/[(x^2+2)^(1/5)]}^(1/5)*(1/5)(1/(x-5)-(2x/(5(x^2+2)))
两边求导数得：
y'/y=(1/5)(1/(x-5)-(1/5)*2x/(x^2+2))
所以：y'={(x-5)/[(x^2+2)^(1/5)]}^(1/5)*(1/5)(1/(x-5)-(2x/(5(x^2+2)))
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