What is the derivative of

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BlackTom AI · Accepted Answer

The problem asks for the derivative of f(x) = 2√(3x - 4).
First, recognize that √(3x - 4) is (3x - 4)^(1/2). The function can be rewritten as f(x) = 2(3x - 4)^(1/2).
Next, apply the chain rule: the derivative of (u)^(1/2) with respect to x is (1/2)u^(-1/2) * du/dx, where u = 3x - 4.
Compute du/dx = d/dx(3x - 4) = 3.
Therefore, d/dx[(3x - 4)^(1/2)] = (1/2)(3x - 4)^(-1/2) * 3 = 3/(2√(3x - 4)).
Now multiply by the constant 2 from the original function: f'(x) = 2 * [3/(2√(3x - 4))].
The factors of 2 cancel, leaving f'(x) = 3/√(3x - 4).
You can also write this as 3(3x - 4)^(-1/2) if you prefer the exponent form.
If you were comparing potential answer forms, ensure the final expression has the square root in the denominator and the numerator as 3, matching the chain rule result.

What is the derivative of

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