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Explore Stack InternalBy definition, $f^{\prime}(z_0) = lim_{z \to z_0} \frac{f(z)-f(z_0)}{z-z_0} $$f^{\prime}(z_0) = \mathrm{lim}_{z \to z_0} \frac{f(z)-f(z_0)}{z-z_0} $
If the function is differentiable, then the limit exists. If the limit exists, then it is independent of how $z \to z_0$. In particular, we could fix $y_0$ and approach along $x$.
By definition, $f^{\prime}(z_0) = lim_{z \to z_0} \frac{f(z)-f(z_0)}{z-z_0} $
If the function is differentiable, then the limit exists. If the limit exists, then it is independent of how $z \to z_0$. In particular, we could fix $y_0$ and approach along $x$.
By definition, $f^{\prime}(z_0) = \mathrm{lim}_{z \to z_0} \frac{f(z)-f(z_0)}{z-z_0} $
If the function is differentiable, then the limit exists. If the limit exists, then it is independent of how $z \to z_0$. In particular, we could fix $y_0$ and approach along $x$.
