Does (f^(-1)(x))’ equal (f^(-1))'(x) because we got "f^(-1)(x)" as a constant and the derivative of a constant is zero. That would be different than the second function right?

Question

anonymous · Answer

clarification: f^(-1) as an inverse

anonymous · Answer

Look at the first two expressions.  In 1 you take the derivative of the function of x and in the other you take the derivative of the function then multiply on the x.  If your function does not contain the variable that you are differentiating to.  Then what are taking the derivative of ? constants?