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Find the derivative of $x^{-1}$ 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 $x^{-1}$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\left(x+h\right)^{-1}-x^{-1}}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of x^(-1) using the definition. Find the derivative of x^{-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 x^{-1}. Substituting f(x+h) and f(x) on the limit, we get. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. . Any expression to the power of 1 is equal to that same expression.