The right response is a) 2ln(3) × 3^(2x).
The power rule of differentiation and the chain rule can be used to determine the derivative of the function f(x) = 3^(2x).
According to the power rule, a function with the formula f(x) = a^g(x) has the following derivative:
d/dx (a^g(x)) = a^g(x) × ln(a) × g'(x)
In this case, we have f(x) = 3^(2x), where a = 3 and g(x) = 2x.
Using the power rule:
f'(x) = d/dx (3^(2x))
= 3^(2x) × ln(3) × 2
= 2ln(3) × 3^(2x)
Consequently, 2ln(3) × 3^(2x) is the derivative of 3^(2x).
The right response is a) 2ln(3) × 3^(2x).
The power rule of differentiation and the chain rule can be used to determine the derivative of the function f(x) = 3^(2x).
According to the power rule, a function with the formula f(x) = a^g(x) has the following derivative:
d/dx (a^g(x)) = a^g(x) × ln(a) × g'(x)
In this case, we have f(x) = 3^(2x), where a = 3 and g(x) = 2x.
Using the power rule:
f'(x) = d/dx (3^(2x))
= 3^(2x) × ln(3) × 2
= 2ln(3) × 3^(2x)
Consequently, 2ln(3) × 3^(2x) is the derivative of 3^(2x).