# Step-by-step Solution

## Find the higher order derivative of $\frac{3}{2}\left(1+\frac{x}{3}\right)^3$

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### Videos

$1+\frac{x}{3}$

## Step-by-step explanation

Problem to solve:

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

Rewriting the high order derivative

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

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

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

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

### Main topic:

Differential calculus

~ 1.1 seconds

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