Question

Calculate the derivative of the function s(x) = 3x - 3^(2x-8/3)?

Answer 1

The derivative of the function s(x) = 3x - 3^(2x-8/3) is 3 + ln(3) * 3^(2x-8/3) * (2).

Step-by-step explanation:

To find the derivative of the given function s(x) = 3x - 3(2x-8/3), we can use the power rule and chain rule of differentiation. Here are the steps:

1. First, differentiate the term 3x using the power rule. The derivative is 3.
2. Next, differentiate the term 3(2x-8/3) using the chain rule, considering it as 3u where u = 2x - 8/3. The derivative is ln(3) * 3(2x-8/3) * (2).
3. Combine the derivatives from steps 1 and 2 to find the overall derivative of the function. It is 3 + ln(3) * 3(2x-8/3) * (2).

Therefore, the derivative of the function s(x) is 3 + ln(3) * 3(2x-8/3) * (2).