A function is homogeneous of degree if for all and . If is also differentiable, show that

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Differentiate the equation $\displaystyle f(tx_1,tx_2,\ldots,tx_n) = t^mf(x)$ partially with respect to t (keeping $\displaystyle x_1,x_2,\ldots,x_n$ constant and using the chain rule), then put t=1.