Question

Find the derivative of tan⁻¹ x with respect to logx; (where x ∈ (1, ∞)).

Answer 1

y = tan⁻¹ x and z = log_e x

Then `dy/dx = 1/(1 + x^2)` and `dz/dx = 1/x`

`dy/dz = (dy/dx)/(dz/dx)`

= `(1/(1 + x^2))/(1/x)`

= `x/(1 + x^2)`