$\"\"$

The composite function is $\"y=\\sin$ .

$\"y\"$ is in the form of composite function $\"f\\$ .

Definition of composite function :

The notation $\"f\\$ means that the function $\"\"$ is applied first and then $\"\"$ is applied.

Consider $\"\\small$ .

$\"y=\\sin$ .

From the above expression, $\"\\small$ and $\"\\small$ .

$\"\"$

$\"y=\\sin$

Differentiate on each side with respect to $\"x\"$ .

Chain Rule of derivatives: $\"\\frac{d}{dx}f(g(x))=$ .

Derivative of the cotangent function: $\"\\frac{d}{dx}(\\cot$ .

$\"\\\\y\'=\\frac{d}{dx}(\\textrm{sin}(\\textrm{cot}(x)))\\\\$

$\"\"$

$\"\\small$ and $\"\\small$ .

$\"\\\\y\'=-\\csc^2x$ .