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:
`(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}`