find derivative of f(x)= x√3?
To find the derivative of the function f(x) = x√3, we can use the power rule of differentiation
To find the derivative of the function f(x) = x√3, we can use the power rule of differentiation.
The power rule states that if we have a function of the form f(x) = x^n where n is any real number, then the derivative of f(x) is equal to n*x^(n-1).
In this case, we have f(x) = x√3 where n = √3. Applying the power rule, we get:
f'(x) = √3 * x^(√3 – 1).
Next, we simplify the exponent (√3 – 1):
To simplify (√3 – 1), we can multiply the numerator and the denominator by the conjugate of the denominator, which is (√3 + 1).
(√3 – 1) * (√3 + 1) = (√3)^2 – 1^2 = 3 – 1 = 2.
Therefore, (√3 – 1) = (2 / (√3 + 1)).
Replacing (√3 – 1) with (2 / (√3 + 1)) in the derivative expression:
f'(x) = √3 * x^(√3 – 1)
= √3 * x^(2 / (√3 + 1)).
Thus, the derivative of f(x) = x√3 is √3 * x^(2 / (√3 + 1)).
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