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Simplify the derivative by applying the properties of logarithms
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$\frac{d}{dx}\left(\sqrt{\frac{x^{-3}}{10-x^2}}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of ((x^(2-5))/(10-x^2))^1/2. Simplify the derivative by applying the properties of logarithms. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}.