Derivative of the inverse function and its application

1. Derivative of the original function is equal to the one over derivative of the inverse function with mirror point of the original function.

2. only if function f(x) is invertible.

3. Volume is an invertible function.

4.

5.

(1) Black :

(2) Red :

(3) Orange: : Tangent line of the V(r)

(4) Green : : Tangent line of the r(V)

6. Combine two tangent line equation

Data table shows that x value and y value is equal; therefore, this two tangent ling function is invertible and the the values of functions are reciprocals.

7. I attended the virtual class, because of the reason that the virtual class gives me more time to spend on the subject, and less pressure from other student.