Question

If y = e^x tan^–1e^x – ℓn √(1 + e^2x) the (dy/dx) is

(a) e^x tan^–1e^x

(b) [e^x/(tan^–1e^x)]

(c) tan^–1e^x

(d) none of these

Answer 1

The correct option (a) e^x tan^–1e^x

Explanation:

y = e^x tan^–1 e^x – (1/2) ℓn (1 + e^2x)

∴ (dy/dx) = e^x ∙ [1/(1 + e^2x)] ∙ e^x + e^x tan^–1e^x – (1/2) [1/(1 + e^2x)] ∙ e^2x ∙ 2

= [(e^2x)/(1 + e^2x)] + e^xtan^–1e^x – [(e^2x)/(1 + e^2x)]

= e^x tan^–1e^x