Asked by Erica
If dy/dx = x²y², then d²y/dx² = ?
Answers
Answered by
Damon
f(x,y) = x^2 y^2
df(x,y)/dx = x^2 (2 y dy/dx) + y^2(2 x dx/dx)
but dy/dx = x^2y^2
so
x^2(2 y x^2y^2) + 2 x y^2
2 x^4 y^3 + 2 x y^2
2 x y^2 (x^2 y + 1)
df(x,y)/dx = x^2 (2 y dy/dx) + y^2(2 x dx/dx)
but dy/dx = x^2y^2
so
x^2(2 y x^2y^2) + 2 x y^2
2 x^4 y^3 + 2 x y^2
2 x y^2 (x^2 y + 1)
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