Differentiation from first principles- need help - cant do at all

  • Thread starter pat666
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  • #1
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Homework Statement


see attachment- have to do this because i cant figure out how to do the notation in this part sorry....... I have no idea where to go with this and probably need quite a bit of help with it--- thanks.


Homework Equations





The Attempt at a Solution

 

Attachments

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Answers and Replies

  • #2
HallsofIvy
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The problem says "use the definition of derivative
[tex]\lim\frac{\delta y}{\delta x}[/tex]

Do you know what that means?
[tex]\frac{\delta y}{\delta x}= \frac{y(1+ \delta x)- y(1)}{\delta x}[/tex]

[itex]y(1)= 1^2- 1= 0[/itex] and [itex]y(1+ \delta x)= (1+ \delta x)^2- (1+ \delta x)[/itex].
 
  • #3
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hey - sorry bud i dont get any of that??? - the lecture that we had talked for about 15s on this and I really dont understand it. more help would be GREATLY appreciated.
 
  • #4
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The derivative definition is usually presented using upper-case delta, [itex]\Delta[/itex] rather than lower-case delta, [itex]\delta[/itex] as you have.

It might be helpful to use function notation, letting f(x) = y = x2 - x. The derivative of f at 1 can be written this way:
[tex]\lim_{\Delta x \to 0} \frac{f(1 + \Delta x) - f(1)}{\Delta x}[/tex]

The fraction gives the slope of a secant line between (1, f(1)) and (1 + [itex]\Delta x[/itex], f(1 + [itex]\Delta x[/itex])). The numerator gives the vertical change (rise) and the denominator gives the horizontal change (run). As [itex]\Delta x[/itex] approaches zero, the slope of the secant line approaches the slope of the tangent line.

Substitute for f(1) and f(1 + [itex]\Delta x[/itex]) in the limit formula above, simplify, and then take the limit.

If you still don't understand, your text should have an explanation of this and some examples.
 
  • #5
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BTW, you should post calculus problems (like this one) in the Calculus & Beyond section.
 

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