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Find the derivative of $9^{\frac{1}{3}}\left(\sqrt{2}+1\right)^{\frac{1}{3}}\left(27-2\sqrt{162}\right)^{\frac{1}{6}}$

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Step-by-step Solution

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  • Find the derivative
  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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Simplifying

$\frac{d}{dx}\left(\sqrt[3]{9}\sqrt[3]{\sqrt[4]{4}+1}\sqrt[6]{27-18\sqrt{2}}\right)$

Learn how to solve differential calculus problems step by step online.

$\frac{d}{dx}\left(\sqrt[3]{9}\sqrt[3]{\sqrt[4]{4}+1}\sqrt[6]{27-18\sqrt{2}}\right)$

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Learn how to solve differential calculus problems step by step online. Find the derivative of 9^(1/3)(2^1/2+1)^(1/3)(27-2162^1/2)^(1/6). Simplifying. Simplifying. The derivative of the constant function (2.2362964\sqrt[3]{\sqrt[4]{4}+1}) is equal to zero.

Final answer to the problem

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Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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