Final answer to the problem
$\frac{1}{2\sqrt{1-x}\sqrt{x}}$
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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
$\frac{1}{\sqrt{1-\left(\sqrt{x}\right)^2}}\frac{d}{dx}\left(\sqrt{x}\right)$
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$\frac{1}{\sqrt{1-\left(\sqrt{x}\right)^2}}\frac{d}{dx}\left(\sqrt{x}\right)$
Learn how to solve problems step by step online. Find the derivative of arcsin(x^(1/2)). Taking the derivative of arcsine. Cancel exponents \frac{1}{2} and 2. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Multiplying fractions \frac{1}{\sqrt{1-x}} \times \frac{1}{2}.
Final answer to the problem
$\frac{1}{2\sqrt{1-x}\sqrt{x}}$
