Question

$find \: \binom{dy}{dx} function \: of \\ {sin}^{2} y + \cos(xy) = k$
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Answer 1

Answer:

sin^(2)y + cos xy = k

<br> Differentiate both sides w.r.t. x <br>

2sin y cos y (dy)/(dx) + (-sin xy) (d)/(dx)(xy) =0

<br>

rArr sin 2y (dy)/(dx)-sin xy(x(dy)/(dx)+ y .1)=0

<br>

rArr (dy)/(dx)(sin2y- x sin xy)= ysin xy

<br>

rArr (dy)/(dx)=(y sin xy)/(sin 2y = x sin xy)

Answer 2

Answer:

sin^(2)y + cos xy = k

<br> Differentiate both sides w.r.t. x <br>

2sin y cos y (dy)/(dx) + (-sin xy) (d)/(dx)(xy) =0

<br>

rArr sin 2y (dy)/(dx)-sin xy(x(dy)/(dx)+ y .1)=0

<br>

rArr (dy)/(dx)(sin2y- x sin xy)= ysin xy

<br>

rArr (dy)/(dx)=(y sin xy)/(sin 2y = x sin xy)