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Simplify the expression $\frac{\sqrt[3]{x}-1}{\sqrt[4]{x}-1}$

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Solution

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Final Answer

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Limit

$\lim_{x\to1}\left(\frac{\sqrt[3]{x}-1}{\sqrt[4]{x}-1}\right)=\frac{4}{3}$ See full solution

Derivative

$\frac{d}{dx}\left(\frac{\sqrt[3]{x}-1}{\sqrt[4]{x}-1}\right)=\frac{-3\sqrt[3]{x}+3+4\left(\sqrt[4]{x}-1\right)\sqrt[12]{x}}{12\sqrt[4]{x^{3}}\left(\sqrt[4]{x}-1\right)^2}$ See full solution

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind (x^0.3333-1)/(x^0.25-1) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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