Final Answer
Step-by-step Solution
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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=2\sqrt{r^2-x^2}$
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$2\frac{d}{dx}\left(x\right)\sqrt{r^2-x^2}+x\frac{d}{dx}\left(2\sqrt{r^2-x^2}\right)$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx(2x(r^2-x^2)^1/2). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=2\sqrt{r^2-x^2}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sqrt{r^2-x^2} and g=2. The derivative of the constant function (2) is equal to zero. Any expression multiplied by 0 is equal to 0.