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Step-by-step Solution

Find the derivative $\frac{d}{dx}\left(9x^4\ln\left(x^4\right)+\ln\left(x\right)^5\right)$ using the sum rule

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Answer

$9\left(4x^{3}\ln\left(x^4\right)+x^{7}\cdot\frac{4}{x^4}\right)+\ln\left(x\right)^{4}\cdot\frac{5}{x}$

Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(9x^4\cdot\ln\left(x^4\right)+\ln\left(x\right)^5\right)$
1

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

$\frac{d}{dx}\left(9x^4\ln\left(x^4\right)\right)+\frac{d}{dx}\left(\ln\left(x\right)^5\right)$
2

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

$9\frac{d}{dx}\left(x^4\ln\left(x^4\right)\right)+\frac{d}{dx}\left(\ln\left(x\right)^5\right)$

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Answer

$9\left(4x^{3}\ln\left(x^4\right)+x^{7}\cdot\frac{4}{x^4}\right)+\ln\left(x\right)^{4}\cdot\frac{5}{x}$
$\frac{d}{dx}\left(9x^4\cdot\ln\left(x^4\right)+\ln\left(x\right)^5\right)$

Main topic:

Sum rule

Used formulas:

6. See formulas

Time to solve it:

~ 0.85 seconds

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