Step-by-step Solution

Find the derivative $\frac{d}{dx}\left(x^2-2x^5\ln\left(x+2\right)\right)$ using the sum rule

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Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(x^2-2x^5\ln\left(x+2\right)\right)$

Learn how to solve sum rule of differentiation problems step by step online.

$\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(-2x^5\ln\left(x+2\right)\right)$

Unlock this full step-by-step solution!

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative (d/dx)(x^2-2x^5*ln(x+2)) using the sum rule. The derivative of a sum of two functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (-2) 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^5 and g=\ln\left(x+2\right). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

Final Answer

$2x-2\left(5x^{4}\ln\left(x+2\right)+\frac{x^5}{x+2}\right)$