Final Answer
$\frac{-1+x}{\sqrt{\left(x-\frac{3}{2}\right)^2+x}}$
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Step-by-step Solution
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Simplifying
$\frac{d}{dx}\left(\sqrt{\left(x-\frac{3}{2}\right)^2+\left(\sqrt{x}\right)^2}\right)$
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$\frac{d}{dx}\left(\sqrt{\left(x-\frac{3}{2}\right)^2+\left(\sqrt{x}\right)^2}\right)$
Learn how to solve problems step by step online. Find the derivative of ((x+-3/2)^2+x^1/2^2)^1/2. Simplifying. Simplify the derivative by applying the properties of logarithms. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of a sum of two or more functions is the sum of the derivatives of each function.
Final Answer
$\frac{-1+x}{\sqrt{\left(x-\frac{3}{2}\right)^2+x}}$