Two functions, f and g, are continuous and differentiable for all real numbers. Some values of the functions and their derivatives are shown in this table:
Based on that luscious table, find the following derivatives:
(a)
(b)
(c)
(d)
Difficulty:
(a) Take the derivative of each function separately (since the derivative of a sum is equal to sum of its derivatives) and plug in 4 to each to get your answer. To find out what the derivatives are when 4 is plugged in for x, just look at the chart:
(b) This time you have to use the Product Rule, since f and g are being multiplied together; once again, after you apply the correct derivative rule, just nab the needed function and derivative values from the chart:
(c) This time it's the Quotient Rule that has to be applied:
(d) Can you say "Chain Rule"? Remember, you apply the Chain Rule when one function is composed with (inside of) another. To derive, take the derivative of the outer function f while leaving g alone inside f. Then multiply by the derivative of g:
