$\"\"$

The function is $\"\"$ .

Apply derivative with respect to $\"\"$ \ \

$\"\"$

$\"\"$ .

The function is $\"\"$ .

The $\"\"$ function is not defined for the odd multiples of $\"\"$

The Domain of the function is $\"\"$ .

Hence the one of the largest interval is $\"\"$ .

$\"\"$

Write the derivative as a function of $\"\"$ .

$\"\"$ .

Since trigonometric identities : $\"\"$

Substitiute $\"\"$ in the function $\"\"$ .

$\"\"$ .

$\"\"$

Substitute $\"\"$ in the function $\"\"$ .

$\"\"$

The derivative of $\"\"$ is $\"\"$ .

The one of the largest interval is $\"\"$ .

The derivative of $\"\"$ in terms of $\"\"$ is $\"\"$ .