Is y' = dy/dx? Solving for dy/dx in a Test Question

Thread starter General_Sax
Start date Dec 13, 2009

In summary, y' represents the derivative of y with respect to x, which is the instantaneous rate of change of y with respect to x at a specific point. To solve for y', one needs to use the rules of differentiation. Y' and dy/dx are two different notations for the same thing and can both be negative or positive. Y' is equal to the slope of the tangent line at a specific point on the graph of the function y.

Dec 13, 2009

General_Sax

I was given a question on a test today to find dy/dx.

both y and x were involved in the expression.

I solved for y'

Did I awnser the question correctly, ie, is y' = dy/dx?

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Dec 13, 2009

boboYO

yes, y' is just another notation.

Dec 13, 2009

HallsofIvy

Science Advisor

Homework Helper

y' was Newton's notation, dy/dx was Leibniz's notation.

1. What does y' represent in the equation dy/dx?

Y' represents the derivative of y with respect to x. It is the instantaneous rate of change of y with respect to x at a specific point.

2. How do you solve for y' in the equation dy/dx?

To solve for y', you need to use the rules of differentiation, which involve finding the derivative of each term in the equation and then simplifying the resulting expression.

3. What is the difference between y' and dy/dx?

Y' and dy/dx are two different notations for the same thing: the derivative of y with respect to x. Some prefer to use y' as a shorthand notation, while others prefer the Leibniz notation of dy/dx.

4. Can y' be negative?

Yes, y' can be negative. This indicates that the function y is decreasing as x increases. If y' is positive, it means that the function is increasing as x increases.

5. How is y' related to the slope of a tangent line?

Y' is equal to the slope of the tangent line at a specific point on the graph of the function y. This is because the derivative represents the rate of change of y at a specific point, which is the same as the slope of the tangent line at that point.