Explain how to determine derivative of function y=2^(2x+3)?

well using the logarithm differentation is right, here is
also another way to do it, which is by the exponent rule and the chain
rule.

The chain rule states that you split a function into
two functions, differentiate the outside function, leave the inside alone, then
differentiate the inside function.

2^(2x+3) is basically
two functions. One is 2^y , another is y=2X+3

we know by
the exponent rule

differentation of A^X (A is a
constant)=A^X ln A

so by the chain
rule

it is ln 2 * 2^ Y * 2

the
two at the end is the dervative of the inside function

well
Y= 2x+3

it is 2*ln2*
2^(2X+3)

btw, the log laws state that 2 ln 2 = ln (2^2)=ln
4

so the derivative
is

ln 4
*(2^(2x+3))