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Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$
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$derivdef\left(-x^{-2}\right)$
Learn how to solve problems step by step online. Find the derivative of -1/(x^2) using the definition. 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. Multiply -1 times -1. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.