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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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$\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(-2x^5\ln\left(x+2\right)\right)$
Learn how to solve problems step by step online. Find the derivative d/dx(x^2-2x^5ln(x+2)) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^5 and g=-2\ln\left(x+2\right). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\ln\left(x+2\right) and g=-2. The derivative of the constant function (-2) is equal to zero.