Final Answer
$\frac{x\left(120-6e^{\frac{1}{100}x}-\frac{3}{100}xe^{\frac{1}{100}x}\right)}{\sqrt[5]{a^{7}}}$
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Step-by-step Solution
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Simplifying
$\frac{d}{dx}\left(\frac{3x^2\left(20-e^{\frac{1}{100}x}\right)}{\sqrt[5]{a^{7}}}\right)$
Learn how to solve product rule of differentiation problems step by step online.
$\frac{d}{dx}\left(\frac{3x^2\left(20-e^{\frac{1}{100}x}\right)}{\sqrt[5]{a^{7}}}\right)$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx((3x^2)/(a^7^1/5)(20-e^(1/100x))). Simplifying. 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. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'. The derivative of the constant function (3) is equal to zero.
Final Answer
$\frac{x\left(120-6e^{\frac{1}{100}x}-\frac{3}{100}xe^{\frac{1}{100}x}\right)}{\sqrt[5]{a^{7}}}$