If $x^2y +yx^3=5x+3 ,$ then $\frac{dy}{dx}= $
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{5-3x^2y-2xy}{x^2+x^3-3}$
$x^2y +yx^3=5x+3$
Differentiating both sides w.r.t. 'x'.
$2xy+x^2\frac{dy}{dx}+3x^2y+x^3\frac{dy}{dx}=5$
$\frac{dy}{dx}(x^2+x^3)=5-2xy-3x^2y$
$⇒\frac{dy}{dx}=\frac{5-2xy-3x^2y}{x^2+x^3}$