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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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$\frac{d}{dx}\left(e^{8x}\right)+\frac{d}{dx}\left(4xe^{8x}\right)$
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(e^(8x)+4xe^(8x)) 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 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=x and g=e^{8x}. The derivative of the linear function is equal to 1.