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The derivative of a sum of two or more functions is the sum of the derivatives of each function
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$\frac{d}{dx}\left(\sqrt[3]{x}\right)+\frac{d}{dx}\left(\sqrt{x}\right)$
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(x^1/3+x^1/2) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. 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 power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.