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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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$\frac{d}{dx}\left(4x^3\right)+\frac{d}{dx}\left(e^{-2x}\right)$
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(4x^3+e^(-2x)) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (4) is equal to the constant times the derivative of the 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}. Applying the derivative of the exponential function.