Question

y= x arctan$(1/x)$

Hallar la derivada

Answer 1

Aplicamos derivada de producto:
y'= (x)'arctan (1/x) + x [arctan (1/x)]'
y'= arctan (1/x) + x [(1/x)'/(1 + (1/x)^2)]
y'= arctan (1/x) + x [(-1/x^2)/(1 + (1/x)^2)]
y'= arctan (1/x) - x/(x^2)(1 + (1/x)^2)
y'= arctan (1/x) - x/(x^2 + 1)