find derivative of f(x)= 3√x?
To find the derivative of the function f(x) = 3√x, we can use the power rule of differentiation
To find the derivative of the function f(x) = 3√x, 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 given by:
f'(x) = n * x^(n-1)
In this case, we can rewrite the function f(x) = 3√x as f(x) = 3x^(1/2), where the exponent 1/2 represents the square root (√).
Now, we can apply the power rule to find the derivative:
f'(x) = (1/2) * 3 * x^(1/2 – 1)
Simplifying further, we get:
f'(x) = (3/2) * x^(-1/2)
Finally, we can rewrite x^(-1/2) as 1/√x:
f'(x) = (3/2) * (1/√x)
So, the derivative of f(x) = 3√x is f'(x) = (3/2) * (1/√x).
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