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

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Solution

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Final Answer

$\frac{120x-6e^{\frac{1}{100}x}x-\frac{3}{100}x^2e^{\frac{1}{100}x}}{\sqrt[5]{a^{7}}}$
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Step-by-step Solution

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Simplify the derivative by applying the properties of logarithms

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

Learn how to solve differential calculus problems step by step online.

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

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Learn how to solve differential calculus 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 (3) 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}.

Final Answer

$\frac{120x-6e^{\frac{1}{100}x}x-\frac{3}{100}x^2e^{\frac{1}{100}x}}{\sqrt[5]{a^{7}}}$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of 3x^2/(a^7^0.2)(20+-1e^0.01x) using the product ruleFind derivative of 3x^2/(a^7^0.2)(20+-1e^0.01x) using the quotient ruleFind derivative of 3x^2/(a^7^0.2)(20+-1e^0.01x) using logarithmic differentiationFind derivative of 3x^2/(a^7^0.2)(20+-1e^0.01x) using the definition

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Plotting: $\frac{120x-6e^{\frac{1}{100}x}x-\frac{3}{100}x^2e^{\frac{1}{100}x}}{\sqrt[5]{a^{7}}}$

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x
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(◻)
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◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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