Thread: does continuity imply partial derivative existance

does continuity of function imply existence of partial derivatives.if not please give an example of such a function.

Originally Posted by saurabhtmz

does continuity of function imply existence of partial derivatives.if not please give an example of such a function.

No.

Look at f(x.y) = |x| + |y| . It's continuous everywhere on ℝ², yet it is not differentiable on the x & y axes.