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The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$
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$\frac{d}{dr}\left(\pi \left(3+r\right)\sqrt{\left(3-r\right)^2+\frac{11664}{\left(9+r^2+3r\right)^2}}\right)$
Learn how to solve problems step by step online. Find the derivative of pi(3+r)((3-r)^2+(108/(9+r^23r))^2)^1/2. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. The derivative of a function multiplied by a constant (\pi ) 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=3+r and g=\sqrt{\left(3-r\right)^2+\frac{11664}{\left(9+r^2+3r\right)^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}.