Calculus 3 Derivative

Question

Given f(x,y)=−4x^4−3x^2y^2−6y6, find fxx(x,y)

Answer 1

For the derivative of f(x,y) with respect to x twice, just treat anything y as a constant.

f_x(x,y) = -16x³-6xy²-0

f_xx(x,y) = -48x²-6y²

Answer 2

Bradford's answer is, of course, correct. The two keys to understanding how to do all of the problems that you listed:

The subscript with f indicates what you are taking the derivative with respect to. When you take the derivative with respect to one variable, you treat all of the other variables as constants.

fx is the derivative with respect to x; fy is the derivative with respect to y; then,

fxx is the second derivative with respect to x; fyy is the second derivative with respect to y; and fxy is the derivative with respect to x, then the derivative of this respect to x and y.