Q: If f(x) = 3x – 12, what if f'(x)?
A: A combination of a power rule and a constant rule.
(1) The derivative of any constant (any plain old number) is 0. Why? Think about a constant graph y = 7, say. This is a flat line. What is the slope (derivative) of a flat line? 0!
(2) What is the derivative of 3x? Use the power rule! 3x^1… Bring down the 1 as a multiplier and subtract 1 from the exponent: 1*3x^(1-1) = 3x^0 = 3. Remember, x^0 = 1 (or anything to the zero power for that matter).
Combining these concepts:
f(x) = 3x – 12 [Take the derivative of each part separately: the derivative of 3x and the derivative of 12]
f'(x) = 3 – 0 = 3.