The **Derivatives of inverse functions **exercise appears within Khan Academy's 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 Edit

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 Edit

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 Edit

1. Finding the tangent line of an inverse function

2. Understanding the rules of Differential calculus

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