$\"\"$

The composite function is $\"y=(2x^3+5)^4\"$ .

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

Consider $\"f\\$ .

Definition of composite function :

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

Consider $\"\\small$ .

$\"y=(2x^3+5)^4=g(x)^4\"$ .

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

$\"\"$

$\"y=(2x^3+5)^4\"$

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

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

$\"\\\\y\'=$

$\"\"$

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

$\"\\\\y\'=24x^2(2x^3+5)^3.\"$