Derivatives of inverse functions

The Derivatives of inverse functions exercise appears under the Differential calculus Math Mission. This exercise strengthens understanding of how to take the derivative of inverse functions, special derivatives, and the product rule.

Types of Problems
There are three types of problems in this exercise

1. Inverse sine: Being able to find the inverse sine and applying the product rule on the operation.

2. Inverse cosine: Being able to find the inverse cosine and applying the product rule on the operation.

3. Inverse tangent: Being able to find the inverse tangent and applying the product rule on the operation.

Strategies
Knowledge of the inverse functions and understanding of the product rule would help to ensure successful completion of this exercise.

1. Inverse Sine: y = sin^-1(x) dy/dx = 1/(sqrt(1-x^2))

2. Inverse Cosine: y = cos^-1(x)

dy/dx = (-1)/(sqrt(1-x^2))

3. Inverse Tangent: y = tan^-1(x)

dy/dx = 1/(1+x^2)

4. Product Rule on two functions: d/dx [f(x)g(x)] = f'(x)g(x) + f(x)g'(x)

5. Product Rule on three functions: d/dx [f(x)g(x)h(x)] = f'(x)g(x)h(x) + f(x)g'(x)h(x) + f(x)g(x)h'(x) 

Real-life Applications
1. Finding the tangent line of an inverse function

2. Understanding the rules of Differential calculus