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Simplify the fraction by $x$
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$derivdef\left(\frac{1}{x}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (x^3)/(x^4) using the definition. Simplify the fraction by x. Find the derivative of \frac{1}{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 \frac{1}{x}. Substituting f(x+h) and f(x) on the limit, we get. Combine \frac{1}{x+h}-\frac{1}{x} in a single fraction. Combine 1+\frac{-\left(x+h\right)}{x} in a single fraction.