Applying the Chain Rule to a Composite Function

$g'(x) = 4(2x^3 + 5)^3 \cdot (2x^3 + 5)$, showing that the derivative involves the outer function’s derivative multiplied by the inner function itself, simplifying nested differentiations.

$g'(x) = 4(2x^3 + 5)^3 \cdot 6x^2$, showing that we first differentiate the outer function (power of 4) and then multiply by the derivative of the inner function, which can be extended to more complex nested functions.

$g'(x) = 4(2x^3 + 5)^3 + 6x^2$, illustrating that we differentiate the outer and inner functions separately and then add them together, which simplifies the process for nested functions.

$g'(x) = (2x^3 + 5)^4 \cdot 6x^2$, demonstrating that we only need to differentiate the inner function and multiply it by the original outer function, regardless of complexity.