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The derivative of a function multiplied by a constant ($2$) is equal to the constant times the derivative of the function
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$2\frac{d}{dx}\left(x\sqrt{r^2-x^2}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of 2x(r^2-x^2)^1/2. The derivative of a function multiplied by a constant (2) 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{r^2-x^2}. The derivative of the linear function is equal to 1. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.