The rule for finding the derivative of y = au is = au(ln a) , where u is a function of x.
Here we will use the Product Rule to find the derivative: f′(x) = x^5 (5x ln 5) + (5x)(5x^4 ), which
simplifies to f′(x) = x^45 x(5 + x ln 5).
SOLUTIONS TO PRACTICE PROBLEM SET 15
1.
First, we take the derivative of y: = 1 − . Next, we find the value of x where y = :
= x + .
With a little algebra, you should get x = 4 or x = . Because x > 1, we can ignore the second
answer. Or, if you are permitted, use your calculator.
Now we can use the formula for the derivative of the inverse of f(x) (see this page):
, where f(a) = c. This formula means that we find the
derivative of the inverse of a function at a value a by taking the reciprocal of the derivative and
plugging in the value of x that makes y equal to a.
2. −
First, we take the derivative of y: = 3 − 15x^2 . Next, we find the value of x where y = 2: 2 =
