Michael J. answered • 04/24/15
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d2/dx2[x2 + 3xy - y2 + 10]
When you see the notation d2/dx2, that means to take the second derivative. So we are actually deriving this function twice. Take the derivative of the original function. Then take the derivative of that derivative. Keep in mind that we are deriving with respect to x, so treat variables other than x as a constant, and the derivative of any constant is always zero.
d2/dx2 is equivalent to d/dx(d/dx).
d/dx(d/dx)[x2 + 3xy - y2 + 10]
d/dx[2x + 3y] =
2
Michael J.
It is because we are taking the derivative of y with respect to x. I think of it as partial differentiation. And implicit differentiation works nicely when you have constant on the other sides of equation. Perhaps, I should have written the problem as
-10 = x2 + 3xy - y2
Then differentiate both sides of equation using implicit differentiation and chain rule twice as you mentioned.
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04/24/15
Mark M.
04/24/15