3 x − 5x^3.
With a little algebra, you should get x = −1. 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.
3.
First, we take the derivative of y: = ex. Next, we find the value of x where y = e : e = ex. It
should be obvious that x = 1.
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.
