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What is the derivative of f(x) = √x?

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Question: What is the derivative of f(x) = √x?

Options:

  1. 1/(2√x)
  2. 2√x
  3. 1/x
  4. √x/2

Correct Answer: 1/(2√x)

Solution: 

f\'(x) = 1/(2√x).

What is the derivative of f(x) = √x?

Practice Questions

Q1
What is the derivative of f(x) = √x?
  1. 1/(2√x)
  2. 2√x
  3. 1/x
  4. √x/2

Questions & Step-by-Step Solutions

What is the derivative of f(x) = √x?
  • Step 1: Understand that we want to find the derivative of the function f(x) = √x.
  • Step 2: Rewrite √x in a different form. We can write it as x^(1/2).
  • Step 3: Use the power rule for derivatives. The power rule states that if f(x) = x^n, then f'(x) = n * x^(n-1).
  • Step 4: Apply the power rule to our function. Here, n = 1/2, so we multiply by 1/2 and decrease the exponent by 1.
  • Step 5: Calculate the derivative: f'(x) = (1/2) * x^(1/2 - 1) = (1/2) * x^(-1/2).
  • Step 6: Rewrite x^(-1/2) in a simpler form. This is the same as 1/(√x).
  • Step 7: Combine everything together: f'(x) = (1/2) * (1/√x) = 1/(2√x).
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