What is the derivative of

Question

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

查看解析

登录即可查看完整答案

类似问题

If 𝑦 = ln ⁡ ( 5 𝑥 − 1 ) 4 then 𝑑 𝑦 𝑑 𝑥 =

Find the velocity at t = 0.69 using the following equation defining position. p(t) = 2t3 - 4t2 +11t -2 Round to 2 decimal places.

Differentiate [ ln ⁡ ( 3 𝑥 ) + 5 ] 2

Differentiate cos 3 ⁡ 4 𝑥

Differentiate 𝑒 3 𝑥 2 + 5 𝑥

Differentiate ln ⁡ ( 𝑥 2 − 5 2 𝑥 + 1 )

Differentiate ln ⁡ ( 7 𝑥 + 5 )

Differentiate cos ⁡ ( 3 𝑥 )

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单