Question

Help with differentials

Consider the function and express the relationship between a small change in x and the corresponding change in y in the form dy=f'(x)dx

f(x)=2x+1

Answer 1

im curious how that is not just a simple case of taking a derivative

Answer 2

the rate of change of a line is the slope of the line .....

Answer 3

ok

Answer 4

I'm having trouble understanding what to do Is the problem. It may not be super difficult I just don't know what to do.

Answer 5

take the derivative of 2x+1, im assuming youve already been taught how to take a derivative. If not, then I assume you already know that the slope of a line defines the change in y per the change in x

Answer 6

yes I know both those things. The derivative and slope is just 2

Answer 7

then dy = 2 dx is how it wants you to express it i believe

Answer 8

o that's all there is to it? lol. I was thinking to myself, they don't give a dx but you're correct that is all they want, thank you.

Answer 9

:) for a more complete run thru
\[y=2x+1\]
\[\frac d{dx}(y=2x+1)\]
\[\frac d{dx}(y)=\frac d{dx}(2x+1)\]
\[\frac {dy}{dx}=\frac {dx}{dx}2\]
\[\frac {dy}{dx}=2\]
\[dy=2~dx\]

Answer 10

ok, thank you