Final answer to the problem
$\frac{\sqrt[3]{2}}{3\sqrt{1-\sqrt[3]{\left(2\right)^{2}}\sqrt[3]{x^{2}}}\sqrt[3]{x^{2}}}$
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Step-by-step Solution
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- 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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1
Taking the derivative of arcsine
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$\frac{1}{\sqrt{1-\left(\sqrt[3]{2x}\right)^2}}\frac{d}{dx}\left(\sqrt[3]{2x}\right)$
Learn how to solve problems step by step online. Find the derivative of arcsin((2x)^(1/3)). Taking the derivative of arcsine. Simplify \left(\sqrt[3]{2x}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{3} and n equals 2. The power of a product is equal to the product of it's factors raised to the same power. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.
Final answer to the problem
$\frac{\sqrt[3]{2}}{3\sqrt{1-\sqrt[3]{\left(2\right)^{2}}\sqrt[3]{x^{2}}}\sqrt[3]{x^{2}}}$
