Question

Find dy/dx by implicit differention.1) x^4 + x^2y^2 + y^3 = 5(2) Sin (x+y) = cosx + casy

Answer 1

Answer:$\frac{dy}{dx}=\frac{-(4x^{3}+2xy^{2})}{2x^{2}y+3y^{2}}$Explanation:

The given equation is:

$x^4+x^2y^2+y^3=5$

The differential is given as:

$4x^3+2xy^2+2yx^2\frac{dy}{dx}+3y^2\frac{dy}{dx}=0$

Make dy/dx the subject of the formula:

$\begin{gathered} 2yx^2\frac{dy}{dx}+3y^2\frac{dy}{dx}=-(4x^3+2xy^2) \\ \\ \frac{dy}{dx}(2x^2y+3y^2)=-(4x^3+2xy^2) \\ \\ \frac{dy}{dx}=\frac{-(4x^3+2xy^2)}{2x^2y+3y^2} \end{gathered}$