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$\frac{d}{dx}\left(-5x^3\sqrt[3]{\frac{27x^{122}}{125y^{3}}}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of -5x^3((27xy^3)/(125x^(-121)y^6))^1/3. Simplifying. 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}. The power of a product is equal to the product of it's factors raised to the same power. Multiplying the fraction by -5x^3.