Behaviour being used: Adaptive mode
Minimum fraction: 0
Question summary: The following statements are based on differentiability of functions of several variables. Check the true statements: The function [Error converting from MathML to accessible text.] is differentiable at any point [Error converting from MathML to accessible text.]; By computing the directional derivative for the function [Error converting from MathML to accessible text.] for any given direction can be deducted that the function is differentiable at the origin; [Error converting from MathML to accessible text.] has its partial derivatives continuous at the origin, hence it is differentiable; The function [f left parenthesis x comma y right parenthesis equals 1 over pi e to the power of x plus y end exponent plus integral subscript 0 superscript x fraction numerator t squared over denominator square root of t to the power of 4 plus 1 end root end fraction dt] is differentiable for all [open parentheses x comma y close parentheses element of real numbers squared]; The function [Error converting from MathML to accessible text.] is not differentiable at the origin and its directional derivatives at the origin equal [Error converting from MathML to accessible text.]; [f left parenthesis x comma y right parenthesis equals square root of open vertical bar xy close vertical bar end root] is not differentiable at the origin
Right answer summary: The function [Error converting from MathML to accessible text.] is differentiable at any point [Error converting from MathML to accessible text.]; [Error converting from MathML to accessible text.] has its partial derivatives continuous at the origin, hence it is differentiable; The function [f left parenthesis x comma y right parenthesis equals 1 over pi e to the power of x plus y end exponent plus integral subscript 0 superscript x fraction numerator t squared over denominator square root of t to the power of 4 plus 1 end root end fraction dt] is differentiable for all [open parentheses x comma y close parentheses element of real numbers squared]; The function [Error converting from MathML to accessible text.] is not differentiable at the origin and its directional derivatives at the origin equal [Error converting from MathML to accessible text.]; [f left parenthesis x comma y right parenthesis equals square root of open vertical bar xy close vertical bar end root] is not differentiable at the origin
Question state: todo