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 $f=x^{-\frac{2}{3}}$ and $g=x+5$
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$\frac{d}{dx}\left(x^{-\frac{2}{3}}\right)\left(x+5\right)+x^{-\frac{2}{3}}\frac{d}{dx}\left(x+5\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of x^(-2/3)(x+5). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^{-\frac{2}{3}} and g=x+5. 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. The derivative of the constant function (5) is equal to zero.