# Math virtual assistant

Calculators Topics Go Premium About Snapxam

# Step-by-step Solution

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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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

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

## Answer

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

### Main topic:

Quotient rule of differentiation

~ 0.78 seconds