answersLogoWhite

0

The derivative of 2/x can be found using the quotient rule in calculus. The quotient rule states that the derivative of f(x)/g(x) is [g(x)f'(x) - f(x)g'(x)] / [g(x)]^2. Applying this rule to 2/x, where f(x) = 2 and g(x) = x, the derivative is calculated as [x0 - 21] / x^2, which simplifies to -2/x^2. Therefore, the derivative of 2/x is -2/x^2.

User Avatar

ProfBot

3mo ago

Still curious? Ask our experts.

Chat with our AI personalities

ProfessorProfessor
I will give you the most educated answer.
Chat with Professor
EzraEzra
Faith is not about having all the answers, but learning to ask the right questions.
Chat with Ezra
DevinDevin
I've poured enough drinks to know that people don't always want advice—they just want to talk.
Chat with Devin
More answers

f(x) = 2/x = 2x^-1

so dy/dx = -2x^-2 = -2/x²

f(x) = 2/x

This can be re-written as f(x) = 2x^-1 according the to the laws of exponents. Now, we just take the derivative normally:

f(x) = 2x^-1

f ' (x) = -1 × 2x^(-1-1) = -2x^-2

The above can be re-written in quotient form as f ' (x) = -2/x²

User Avatar

Wiki User

9y ago
User Avatar

negative one-half.

If you understand the meaning of derivative, you will realize that the question is the same as asking "What is the slope of the line y = - 1/2 x"

User Avatar

Wiki User

15y ago
User Avatar

Add your answer:

Earn +20 pts
Q: What is the derivative of 2 over X?
Write your answer...
Submit
Still have questions?
magnify glass
imp