Let arcsin : [−1, 1] → [−π/2, π/2] be the inverse function of sin : [−π/2, π/2] → [−1, 1]. Showthat arcsin is differentiable on (−1, 1)

Question

Let arcsin : [−1, 1] → [−π/2, π/2] be the inverse function of sin : [−π/2, π/2] → [−1, 1]. Showthat arcsin is differentiable on (−1, 1)
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Solution 1

To show that arcsin is differentiable on (-1,1), we need to show that its derivative exists on this interval.

Step 1: Define the function Let's define the function f(x) = arcsin(x). We want to find f'(x).

Step 2: Use the definition of the derivative The derivative of a function at a certain point Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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