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The power of a product is equal to the product of it's factors raised to the same power
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$\frac{d}{dx}\left(x^2\left(9-x^2\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (x(9-x^2)^1/2)^2. The power of a product is equal to the product of it's factors raised to the same power. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^2 and g=9-x^2. 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.