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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)

Find the derivative of (3x^2)/(a^7^(1/5))(20-1e^(1/100x))

Answer

$\frac{-\frac{3}{100}x^2e^{\frac{1}{100}x}}{\sqrt[5]{a^{7}}}+\frac{60\sqrt[5]{a^{7}}\cdot\frac{d}{dx}\left(x^2\right)-3e^{\frac{1}{100}x}\sqrt[5]{a^{7}}\cdot\frac{d}{dx}\left(x^2\right)}{\sqrt[5]{a^{14}}}$

Step-by-step explanation

Problem

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

Applying the power of a power property

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

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Answer

$\frac{-\frac{3}{100}x^2e^{\frac{1}{100}x}}{\sqrt[5]{a^{7}}}+\frac{60\sqrt[5]{a^{7}}\cdot\frac{d}{dx}\left(x^2\right)-3e^{\frac{1}{100}x}\sqrt[5]{a^{7}}\cdot\frac{d}{dx}\left(x^2\right)}{\sqrt[5]{a^{14}}}$

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

Main topic:

Differential calculus

Used formulas:

4. See formulas

Time to solve it:

~ 2.43 seconds