Final answer to the problem
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How should I solve this problem?
- 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
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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The power of a product is equal to the product of it's factors raised to the same power
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$\frac{d}{dx}\left(\frac{\left(\sqrt[5]{x}\right)^{10}\left(\sqrt{y^{3}}\right)^{10}}{\left(y^{-\frac{2}{5}}\right)^5\left(\sqrt[3]{x^{2}}\right)^5}\right)$
Learn how to solve problems step by step online. Find the derivative of ((x^(1/5)y^(3/2))^10)/((y^(-2/5)x^(2/3))^5). The power of a product is equal to the product of it's factors raised to the same power. Simplify \left(y^{-\frac{2}{5}}\right)^5 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals -\frac{2}{5} and n equals 5. Simplify \left(\sqrt[3]{x^{2}}\right)^5 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{2}{3} and n equals 5. Simplify \left(\sqrt[5]{x}\right)^{10} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{5} and n equals 10.
