Question

求y=e^arctan(1/x)的导数

Answer 1

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)