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y=(1/1+x∧2)e∧arctanx对Y求导怎么做的
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y=(1/1+x∧2)e∧arctanx 对Y求导怎么做的
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答案和解析
y=1/(1+x^2) *e^arctanx
y'=(1/(1+x^2))'e^arctanx+1/(1+x^2)(e^arctanx)'
=1/(1+x^2)^2*(1+x^2)'*e^arctanx+1/(1+x^2)*e^arctanx*(arctanx)'
=2xe^arctanx /(1+x^2)^2 +e^arctanx/(1+x^2) *1/(1+x^2)
=(2x+1)e^arctanx/(1+x^2)^2
y'=(1/(1+x^2))'e^arctanx+1/(1+x^2)(e^arctanx)'
=1/(1+x^2)^2*(1+x^2)'*e^arctanx+1/(1+x^2)*e^arctanx*(arctanx)'
=2xe^arctanx /(1+x^2)^2 +e^arctanx/(1+x^2) *1/(1+x^2)
=(2x+1)e^arctanx/(1+x^2)^2
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