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Find the derivative of $-\frac{1}{2}$ 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 $-\frac{1}{2}$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{-\frac{1}{2}+\frac{1}{2}}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of 8x^2+4x=-1/2 using the definition. Find the derivative of -\frac{1}{2} 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 -\frac{1}{2}. Substituting f(x+h) and f(x) on the limit, we get. Subtract the values \frac{1}{2} and -\frac{1}{2}. Zero divided by anything is equal to zero. The limit of a constant is just the constant.