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What is the derivative of sin^(-1)(x)?
What is the derivative of sin^(-1)(x)?
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Practice Questions
1 question
Q1
What is the derivative of sin^(-1)(x)?
1/√(1-x^2)
-1/√(1-x^2)
1/x
0
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The derivative of sin^(-1)(x) is 1/√(1-x^2)
Questions & Step-by-step Solutions
1 item
Q
Q: What is the derivative of sin^(-1)(x)?
Solution:
The derivative of sin^(-1)(x) is 1/√(1-x^2)
Steps: 5
Show Steps
Step 1: Understand what sin^(-1)(x) means. It is the inverse sine function, also known as arcsin(x).
Step 2: Recall the definition of the derivative. The derivative measures how a function changes as its input changes.
Step 3: Use the formula for the derivative of the inverse sine function. The formula is: d/dx [sin^(-1)(x)] = 1/√(1-x^2).
Step 4: Apply the formula directly to find the derivative of sin^(-1)(x).
Step 5: Write down the final answer: The derivative of sin^(-1)(x) is 1/√(1-x^2).
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