Differentiate with respect to x : tan-1 ( e2x + 1 / e2x - 1 ) The answer: - Maths - Continuity and Differentiability

Question

Differentiate with respect to x :

tan-1 ( e2x + 1 / e2x - 1 )

The answer: -2e2x / ( 1 + e4x )

Manbar Singh · Accepted Answer

Let y = tan-1e2x+1e2x-1put e2x = cot θ⇒y = tan-1cot
θ + 1cot θ - 1⇒y = tan-1cos θsin θ+1cos
θsin θ-1⇒y = tan-1cos θ + sinθcos θ
- sin θ⇒y = tan-11 + tan θ1 - tan θ⇒y =
tan-1tanπ/4 + tan θ1 - tanπ/4 tan θ⇒y =
tan-1tanπ4 + θ⇒y = π4 + θ⇒y =
π4 + cot-1e2x⇒dydx = 0 - 11 + e2x2 × e2x ×
2⇒dydx = -2e2x1 + e4x