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

Derive the function x^4ln(x^4)*9+ln(x)^5 with respect to x

Answer

$\frac{5\ln\left(x\right)^{4}}{x}+\frac{9x^4\frac{d}{dx}\left(x^4\right)}{x^4}+36\ln\left(x\right)\frac{d}{dx}\left(x^4\right)$

Step-by-step explanation

Problem

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

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

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

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Answer

$\frac{5\ln\left(x\right)^{4}}{x}+\frac{9x^4\frac{d}{dx}\left(x^4\right)}{x^4}+36\ln\left(x\right)\frac{d}{dx}\left(x^4\right)$

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

Main topic:

Differential calculus

Used formulas:

5. See formulas

Time to solve it:

~ 1.51 seconds