Final answer:
The derivative of the function g(x) = 2.8ˣ + π² is 2.8ˣln(2.8), since the derivative of a constant is zero and the term 2.8ˣ is differentiated using the exponential rule.
Step-by-step explanation:
The student is asking for the derivative of the function g(x) = 2.8ˣ + π². To find this derivative, we can apply the rules of differentiation.
Firstly, we recognize that π² is a constant, and the derivative of a constant is zero. Next, we look at the term 2.8ˣ. To differentiate this term, we will use the exponential differentiation rule. The derivative of aˣ, where a is a constant and e is the base of the natural logarithms, is aˣln(a). Therefore, the derivative of 2.8ˣ is 2.8ˣln(2.8).
Hence, the derivative of g(x) = 2.8ˣ + π² is 2.8ˣln(2.8).