$\"\"$

The function is $\"\"$

$\"\"$ (Apply derivative with respect to t)

$\"\"$ (Apply the sum and difference rule)

$\"\"$ (The power rule: $\"\"$ )

$\"\"$ (The product rule)

$\"\"$

$\"\"$ (Take out common terms $\"\"$ and $\"\"$ )

$\"\"$

Therefore the differentiate with respect to t is $\"\"$ .