Question

Question 8:Find dy/dx : sin2 x + cos2 y = 1

Class 12 - Math - Continuity and Differentiability

Answer 1

Differentiation of implicit functions
×××××××××××××××
Sin2x + cos2y= 1
differentiating w.r.x

2sin2x -2sin2y (dy/dx) = 0 { d/dx(sinx) = cosx
d/dx(cosx) = -sinx
2sin2x = 2sin2y (dy/dx)
dy/dx = sin2x/sin2y

Answer 2

★ DIFFERENTIATION ★

Given function :

Sin 2x + Cos 2y = 1

dy( Sin 2x ) /dy = 2 Cos 2x

dy( Cos 2y ) / dx = -2 Sin 2y( dy/dx )

2 Cos x - 2 Sin2y dy/dx = 0

2 Cos2x = 2 Sin 2y dy/dx

dy/dx = 2 Cos 2x / 2sin 2y

Hence , dy/ dx = Cos 2x / Sin 2y

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