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

Find dy/dx by implicit differention.1) x^4 + x^2y^2 + y^3 = 5(2) Sin (x+y) = cosx-example-1
User AngelSalazar
by
3.3k points

1 Answer

24 votes
24 votes
Answer:
(dy)/(dx)=(-(4x^(3)+2xy^(2)))/(2x^(2)y+3y^(2))Step-by-step explanation:

The given equation is:


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

The differential is given as:


4x^3+2xy^2+2yx^2(dy)/(dx)+3y^2(dy)/(dx)=0

Make dy/dx the subject of the formula:


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

User LeleMarieC
by
2.5k points
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