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Simplify the derivative by applying the properties of logarithms
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$\frac{d}{dx}\left(\frac{3x^2\left(20-e^{\frac{1}{100}x}\right)}{\sqrt[5]{a^{7}}}\right)$
Learn how to solve problems step by step online. Find the derivative of (3x^2)/(a^7^1/5)(20-e^(1/100x)). Simplify the derivative by applying the properties of logarithms. The derivative of a function multiplied by a constant (\frac{1}{\sqrt[5]{a^{7}}}) is equal to the constant times the derivative of the function. The derivative of a function multiplied by a constant 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^2 and g=20-e^{\frac{1}{100}x}.