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What is the derivative of \( y = \tan^{-1}(x) \)?
What is the derivative of \( y = \tan^{-1}(x) \)?
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Practice Questions
1 question
Q1
What is the derivative of \( y = \tan^{-1}(x) \)?
\( \frac{1}{1+x^2} \)
\( \frac{1}{x^2+1} \)
\( \frac{1}{x} \)
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The derivative of \( y = \tan^{-1}(x) \) is \( \frac{1}{1+x^2} \).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the derivative of \( y = \tan^{-1}(x) \)?
Solution:
The derivative of \( y = \tan^{-1}(x) \) is \( \frac{1}{1+x^2} \).
Steps: 5
Show Steps
Step 1: Understand that we want to find the derivative of the function y = tan^(-1)(x).
Step 2: Recall that the derivative of a function gives us the rate of change of that function.
Step 3: Use the known formula for the derivative of the inverse tangent function, which is: d/dx(tan^(-1)(x)) = 1/(1+x^2).
Step 4: Apply this formula directly to our function y = tan^(-1)(x).
Step 5: Write down the result: The derivative of y = tan^(-1)(x) is y' = 1/(1+x^2).
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