Question
If x > 0, find the derivative of f(x) = √x
Answers
GPT 3.5
To find the derivative of f(x) = √x when x > 0, we will use the power rule for differentiation.
Given f(x) = √x, we can rewrite it as f(x) = x^(1/2).
Now, we can differentiate f(x) = x^(1/2) with respect to x:
f'(x) = (1/2)x^(-1/2)
f'(x) = 1/(2√x)
Therefore, the derivative of f(x) = √x when x > 0 is f'(x) = 1/(2√x).
Given f(x) = √x, we can rewrite it as f(x) = x^(1/2).
Now, we can differentiate f(x) = x^(1/2) with respect to x:
f'(x) = (1/2)x^(-1/2)
f'(x) = 1/(2√x)
Therefore, the derivative of f(x) = √x when x > 0 is f'(x) = 1/(2√x).