Chantal Nyiransabimana
Feb 4
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Feb 4
To find the differentiation of f(x) = √x, we can use the power rule for differentiation.
The power rule states that if we have a function of the form f(x) = x^n, where n is a constant, then the derivative of f(x) is given by:
f'(x) = n * x^(n-1)
In this case, we have f(x) = √x, which can also be written as f(x) = x^(1/2). Applying the power rule, we get:
f'(x) = (1/2) * x^((1/2)-1)
Simplifying the exponent, we have:
f'(x) = (1/2) * x^(-1/2)
To simplify further, we can rewrite x^(-1/2) as 1/√x:
f'(x) = (1/2) * (1/√x)
Therefore, the differentiation of f(x) = √x is f'(x) = (1/2) * (1/√x).
The power rule states that if we have a function of the form f(x) = x^n, where n is a constant, then the derivative of f(x) is given by:
f'(x) = n * x^(n-1)
In this case, we have f(x) = √x, which can also be written as f(x) = x^(1/2). Applying the power rule, we get:
f'(x) = (1/2) * x^((1/2)-1)
Simplifying the exponent, we have:
f'(x) = (1/2) * x^(-1/2)
To simplify further, we can rewrite x^(-1/2) as 1/√x:
f'(x) = (1/2) * (1/√x)
Therefore, the differentiation of f(x) = √x is f'(x) = (1/2) * (1/√x).
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