Find the derivative $\frac{d}{dx}\left(16\sqrt{2-x^2}+\frac{-8\left(\sqrt{2-x^2}\right)^3}{3}-8x^2\sqrt{2-x^2}\right)$ using the sum rule

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$\frac{d}{dx}\left(16\sqrt{2-x^2}+\frac{-8\sqrt{\left(2-x^2\right)^{3}}}{3}-8x^2\sqrt{2-x^2}\right)$

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(16(2-x^2)^1/2+(-8(2-x^2)^1/2^3)/3-8x^2(2-x^2)^1/2) using the sum rule. Simplify the derivative by applying the properties of logarithms. 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 (16) is equal to the constant times the derivative of the function. The derivative of a function multiplied by a constant (-8) is equal to the constant times the derivative of the function.