If y=cos inverse (sinx+cosx/ root 2) where - pi/4 x pi/4, then find dy/dx - Maths - Continuity and Differentiability

Question

If y=cos inverse (sinx+cosx/ root 2) where -
pi/4<x<pi/4, then find dy/dx

Manbar Singh · Accepted Answer

Dear Student,

Please find below the solution to the asked query :

Let y = cos-1sin x + cos x2⇒y = cos-112 
 sin x + 12
 cos x⇒y = cos-1sinπ4 
 sin x + cosπ4 
 cos x⇒y = cos-1cosπ4 - x⇒y = π4 - x⇒dydx = -1

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If y=cos inverse (sinx+cosx/ root 2) where - pi/4<x<pi/4, then find dy/dx.