Which of the following statements are correct?

Question

BlackTom AI · Accepted Answer

Consider the two differentiation formulas presented as candidate statements.
Option 1: (d/dx)[f(x)/g(x)] = [f'(x)g(x) - f(x)g'(x)] / [g(x)]^2.
This is the quotient rule, which applies when differentiating a ratio of two functions. The numerator combines the derivative of the numerator times the denominator minus the numerator times the derivative of the denominator, while the denominator is the square of the original denominator. This matches the standard quotient rule, so this statement is correct.
Option 2: d/dx [f(x)g(x)] = f'(x)g(x) + f(x)g'(x).
This is the product rule, which describes how to differentiate a product of two functions. You multiply the derivative of the first by the second plus the first times the derivative of the second. This exactly reflects the standard product rule, so this statement is also correct.
In summary, both presented formulas are correct differentiation rules: Option 1 is the quotient rule, and Option 2 is the product rule. The two statements do not contradict each other; they simply apply to different types of composite functions.

EM_MNS1b Week 3 practice quiz

Which of the following statements are correct?

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