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Step-by-step Solution

Find the derivative using the quotient rule $\frac{d}{dx}\left(\frac{3x^2}{2y}\right)$

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Answer

$\frac{3x}{y}$

Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\frac{3x^2}{2y}\right)$
1

Take $\frac{3}{2}$ out of the fraction

$\frac{d}{dx}\left(\frac{\frac{3}{2}x^2}{y}\right)$
2

Applying the quotient rule which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by ${\displaystyle h(x) = \frac{f(x)}{g(x)}}$, where ${g(x) \neq 0}$, then ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

$\frac{y\frac{d}{dx}\left(\frac{3}{2}x^2\right)-\frac{3}{2}x^2\frac{d}{dx}\left(b\right)}{y^2}$

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Answer

$\frac{3x}{y}$
$\frac{d}{dx}\left(\frac{3x^2}{2y}\right)$

Main topic:

Quotient rule of differentiation

Used formulas:

4. See formulas

Time to solve it:

~ 0.78 seconds