How do I deal with square roots and derivatives? Like: f(x)= Sqrtx....the derivative. find
Treat sqrt(x) as x^(1/2) and use the same derivative rule as you would use for any constant power of x.
The derivative is (1/2)x^(-1/2)
= 1/[2sqrt(x)]
To find the derivative of a function with a square root, such as f(x) = √x, you can use the power rule.
The power rule states that if you have a function in the form f(x) = x^n, where n is a constant, then the derivative of the function is given by f'(x) = nx^(n-1).
In the case of f(x) = √x, we can rewrite it as f(x) = x^(1/2). Now, let's find the derivative.
Step 1:
Apply the power rule by multiplying the exponent (1/2) by the coefficient in front of x, which is 1/2.
f'(x) = (1/2) * x^((1/2) - 1)
Step 2:
Simplify the exponent.
f'(x) = (1/2) * x^(-1/2)
Step 3:
Simplify further by moving the term with a negative exponent to the denominator.
f'(x) = (1/2) / √x
Therefore, the derivative of f(x) = √x is f'(x) = (1/2) / √x or f'(x) = (1/2√x).
You can also express the derivative as f'(x) = 1/(2√x). Both forms are equivalent.