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** Step-by-step Solution **

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Find the derivative of $x<y<0$ using the definition. Apply the definition of the derivative: $\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$. The function $f(x)$ is the function we want to differentiate, which is $x<y<0$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get

Learn how to solve definition of derivative problems step by step online.

$\lim_{h\to0}\left(\frac{x+h<y<0-x<y<0}{h}\right)$

Learn how to solve definition of derivative problems step by step online. Find the derivative of x<y<0 using the definition. Find the derivative of x<y<0 using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is x<y<0. Substituting f(x+h) and f(x) on the limit, we get. Cancel like terms x+h<y<0 and -x<y<0. Zero divided by anything is equal to zero. The limit of a constant is just the constant.

** Final Answer

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