Answer to Question #156812 in Calculus for Eliza May

Question #156812

At the point (1,2) on the curve 4x²+2xy+y²=2 dy/dx = ? and d²y/dx² = ?


1
Expert's answer
2021-01-21T11:19:44-0500

Differentiating we get, "8x dx+2y dx +2xdy+2ydy=0". Hence "(x+y)dy=-(y+4x)dx." Hence "dy\/dx=-\\frac{y+4x}{x+y}."

Hence "d^2y\/dx^2=" "-\\frac{(dy\/dx+4)(x+y)-(y+4x)(1+dy\/dx)}{(x+y)^2 }" . Putting the value of "dy\/dx" we get,

"-\\frac{3y^2+12x^2+6xy}{(x+y)^3}" .


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