State and prove sufficient condition for differentiability of the function f(x,y).
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Answer Posted / Mala Shakya
A function f(x, y) is said to be differentiable at a point (a, b) if both the limits:nnlim (h->0) [f(a+h,b) - f(a,b)]/h exist and are equal. In other words, if the limit of the difference quotient exists and is independent of the direction in which h approaches 0, then f(x, y) is differentiable at (a, b). This condition can be expressed in terms of partial derivatives as:nnf_x(a,b) = lim (h->0) [f(a+h,b) - f(a,b)]/h and f_y(a,b) = lim (k->0) [f(a,b+k) - f(a,b)]/k
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