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The derivative of a function multiplied by a constant ($\frac{1}{2}$) is equal to the constant times the derivative of the function
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$\frac{1}{2}\frac{d}{dx}\left(x\sqrt{4-x^2}+4\arcsin\left(\frac{x}{2}\right)\right)$
Learn how to solve problems step by step online. Find the derivative of 1/2(x(4-x^2)^1/2+4arcsin(x/2)). The derivative of a function multiplied by a constant (\frac{1}{2}) is equal to the constant times the derivative of the function. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (4) is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\sqrt{4-x^2}.