学帮网求y=e^arctan(1/x)的导数
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求y=e^arctan(1/x)的导数
须知(e^x)'=e^x,(arctanx)'=1/(1+x²)
y=e^arctan(1/x)
y'=e^arctan(1/x)·1/[1+(1/x)²]·(-1/x²)
=e^arctan(1/x)·x²/(1+x²)·(-1/x²)
=e^arctan(1/x)·-1/(1+x²)
=-e^arctan(1/x)/(1+x²)
=-e^arccot(x)/(1+x²)