# Step-by-step Solution

## Find the derivative using the product rule $\frac{d}{dx}\left(\frac{3x^2}{\left(a^7\right)^{\left(\frac{1}{5}\right)}}\left(20-e^{\frac{1}{100}x}\right)\right)$

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## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\frac{3x^2}{\sqrt[5]{a^{7}}}\cdot\left(20-e^{\frac{1}{100} x}\right)\right)$
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Applying the power of a power property

$\frac{d}{dx}\left(\frac{3x^2}{\sqrt[5]{a^{7}}}\left(20-e^{\frac{1}{100}x}\right)\right)$
2

Multiplying polynomials $\frac{3x^2}{\sqrt[5]{a^{7}}}$ and $20+-e^{\frac{1}{100}x}$

$\frac{d}{dx}\left(\frac{60x^2}{\sqrt[5]{a^{7}}}+\frac{-3e^{\frac{1}{100}x}x^2}{\sqrt[5]{a^{7}}}\right)$

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$\frac{d}{dx}\left(\frac{3x^2}{\sqrt[5]{a^{7}}}\cdot\left(20-e^{\frac{1}{100} x}\right)\right)$

Product rule

~ 0.88 seconds

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