How do you know which rule to use when it doesn't specify? All it says is find the derivative of the function. I haven't had algebra/calculus in over 20 years, I'm completely lost. Please help

Time to review the rules for derivatives. It's a bit of a pain to go back to first principles every time.

I understand that it can be challenging to determine which rule to use when finding the derivative of a function, especially if it hasn't been specified in the question. However, there are a few general strategies you can follow to determine the appropriate rule to apply.

1. Start with the simplest rule: If the function is a basic polynomial (e.g., f(x) = x^n), a constant multiple of a basic polynomial (e.g., f(x) = kx^n, where k is a constant), or a constant (e.g., f(x) = c), you can use the power rule, which states that for any term of the form x^n, the derivative is nx^(n-1).

2. Look for familiar functions or patterns: If the function is a trigonometric function (e.g., sin(x), cos(x), tan(x)), an exponential function (e.g., e^x, 2^x), or a logarithmic function (e.g., ln(x), log(x)), you can use the corresponding derivatives specific to those functions. Familiarity with these derivatives will come with practice and exposure to these functions.

3. Use combination rules: If the function is a combination of different functions, you can utilize various derivative rules to simplify and differentiate the function accordingly. Some common combination rules include the sum/difference rule, the product rule, and the chain rule. These rules allow you to find the derivative of more complex functions by breaking them down into simpler parts.

If you are unsure about which rule to apply, you can also try differentiating the function using multiple rules to see which one yields the correct result.

It's worth mentioning that practice and familiarity with various functions and their derivatives will ultimately help you become more comfortable with determining the appropriate rule to use when finding derivatives. Don't hesitate to use resources such as textbooks, online tutorials, or consult with a math teacher or tutor for additional guidance.