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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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Answer

$2x-2\left(5x^{4}\ln\left(x+2\right)+x^5\frac{1}{x+2}\right)$

Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(x^2-2x^5\ln\left(x+2\right)\right)$
1

The derivative of a sum of two functions is the sum of the derivatives of each function

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

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

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

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Answer

$2x-2\left(5x^{4}\ln\left(x+2\right)+x^5\frac{1}{x+2}\right)$
$\frac{d}{dx}\left(x^2-2x^5\ln\left(x+2\right)\right)$

Main topic:

Sum rule

Used formulas:

7. See formulas

Time to solve it:

~ 0.91 seconds