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Subtract the values $3$ and $-1$
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$derivdef\left(\frac{1}{x^{2}}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of 1/(x^(3-1)) using the definition. Subtract the values 3 and -1. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. Find the derivative of x^{-2} 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^{-2}. 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.