Differentiate w r t x : y = tan-1[ (under root 1 + a2x2) - 1 / ax ] - Maths - Continuity and Differentiability

Question

Differentiate w r t x : y = tan-1[ (under root 1 +
a2x2) - 1 / ax ]

Anuradha Sharma · Accepted Answer

The correct format for this question is, y = tan-11+a2x2-1axLet ax =tanαy =  tan-11+tan2α-1tanα=  tan-1sec2α-1tanα=tan-11cosα-1sinαcosα=tan-11-cosαsinα=tan-11-1+2sin2α22sinα2cosα2=tan-1tanα2=α2=12tan-1axSo dydx=12×11+ax2ddxax=a21+a2x2

Differentiate w.r.t. x : y = tan-1[ (under root 1 + a2x2) - 1 / ax ]

Differentiate w.r.t. x : y = tan^-1[ (under root 1 + a²x²) - 1 / ax ]