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Find (dy)/(dx) in the following:a x+b y...

Find `(dy)/(dx)` in the following:`a x+b y^2=cosy`

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`ax + by^2 = cos y`

Differentiating both sides w.r.t.x

`(d(ax+by^2))/dx = (d(cos y))/dy`

`(d(ax))/dx` + `(d(by^2))/dx` = `(d(cos y))/dx`

`a(dx)/dx` + `b(d(y^2))/dx` = `(d(cos y))/dx`

`a+b(d(y^2))/dx` `xx (dy)/dy` = `(d(cos y))/dx` `xx (dy)/dy`

`a+b (d(y^2))/dy` `xx (dy)/dx` = `(d(cos y))/dy` `xx (dy)/dx` `a+b .2y xx (dy)/dx = -siny (dy)/dx`

`a+ 2by.(dy)/dx = -sin y (dy)/dx`

`2by. (dy)/dx + sin y (dy)/dx = 0-a`

`(dy)/dx (2by+sin y) = -a`

`(dy)/dx = (-a)/(2by +sin y)`
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