$\"\"$

The function is $\"\"$ .

Find the thousandth derivative of the function.

$\"\"$ .

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

Product rule : $\"\"$ .

$\"\"$

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

$\"\"$ .

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

Determine the formula for $\"\"$ derivative of the function $\"\"$ .

Observe the pattern of above three derivatives.

$\"\"$

Substitute $\"\"$ in above expression.

$\"\"$

$\"\"$ .

$\"\"$

$\"\"$ .