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Any expression multiplied by $0$ is equal to $0$
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$derivdef\left(0\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of y+2=0(x-3) using the definition. Any expression multiplied by 0 is equal to 0. Find the derivative of 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 0. Substituting f(x+h) and f(x) on the limit, we get. Add the values 0 and 0. Zero divided by anything is equal to zero.