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Any expression to the power of $1$ is equal to that same expression
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$derivdef\left(1x\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of 1x^1 using the definition. Any expression to the power of 1 is equal to that same expression. Any expression multiplied by 1 is equal to itself. Find the derivative of x 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. Substituting f(x+h) and f(x) on the limit, we get. Cancel like terms x and -x.