If `3sin(x y)+4cos(x y)=5` , then `(dy)/(dx)=` (a)` y/x` (b) `(3sin(x y)+4cos(x y))/(3cos(x y)-4sin(x y))` (c) `(3cos(x y)+4sin(x y))/(4cos(x y)-3sin(x y))` (d) none

Explanation

Differentiate w.r.t.x


`3 cos xy (d/dx)(xy) – 4 sin (xy) d/dx(xy) = 0`


`[3 cos xy – 4 sin (xy) ](d/dx)(xy) = 0`

`[3 cos xy – 4 sin (xy) ](x frac{dy}{dx} + y) = 0`

`frac{dy}{dx} x [3 cos xy – 4 sin (xy) ] = -y [3 cos xy – 4 sin (xy) ]`

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