Generally, you’ll have to take only first and second derivatives.
Notice how we simplified the derivatives in the latter example?
You should be able to do this mentally.Here are some sample problems involving the rules we discussed above. As you work, cover the answers
with an index card, and then check your work after you’re done. By the time you finish them, you should
know the rules by heart.
PROBLEM 1. If y = 50x^5 + − 7x
−
, then =Answer: + =
PROBLEM 2. If y = 9x^4 + 6x^2 − 7x + 11, then =
Answer: = 9(4x^3 ) + 6(2x) − 7(1) + 0 = 36x^3 + 12x − 7
PROBLEM 3. If f(x) = , then f′(x) =
Answer:
How’d you do? Did you notice the changes in notation? How about the fractional powers, radical signs,
and x’s in denominators? You should be able to switch back and forth between notations, between
fractional powers and radical signs, and between negative powers in a numerator and positive powers in
a denominator.