Derivatives of inverse functions, logarithms, and exponentials

The original function and its derivative

tan^-1(x)/arctan(u)

u’/1 + u²

sin^-1(x)/arcsin(u)

1/sqroot(1 - u²)

a^u

a^u(lna)(u’)

log_a(u)

u’/uln(a)

Critical Numbers

Input values where f’=0 or f’ is undefined. The numbers have to be within the domain.

Finding critical numbers

1. Find the derivative of the function

2. Factor the derivative of the function

3. Set the factored version equal to zero (0)

4. Split the factored in two if needed then set both sides equal to zero (0)

5. The x value found after setting the function equal to zero, and are within the domain are the critical numbers