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What is the derivative of f(x) = √x?
What is the derivative of f(x) = √x?
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Practice Questions
1 question
Q1
What is the derivative of f(x) = √x?
1/(2√x)
2√x
1/x
√x/2
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f'(x) = 1/(2√x).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the derivative of f(x) = √x?
Solution:
f'(x) = 1/(2√x).
Steps: 7
Show Steps
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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