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Any expression (except $0$ and $\infty$) to the power of $0$ is equal to $1$
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$derivdef\left(1\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of x^0 using the definition. Any expression (except 0 and \infty) to the power of 0 is equal to 1. Find the derivative of 1 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 1. Substituting f(x+h) and f(x) on the limit, we get. Subtract the values 1 and -1. Zero divided by anything is equal to zero.