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

1. Jul 14, 2010

pat666

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. The attempt at a solution

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2. Jul 15, 2010

HallsofIvy

The problem says "use the definition of derivative
$$\lim\frac{\delta y}{\delta x}$$

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

$y(1)= 1^2- 1= 0$ and $y(1+ \delta x)= (1+ \delta x)^2- (1+ \delta x)$.

3. Jul 15, 2010

pat666

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. Jul 15, 2010

Staff: Mentor

The derivative definition is usually presented using upper-case delta, $\Delta$ rather than lower-case delta, $\delta$ 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:
$$\lim_{\Delta x \to 0} \frac{f(1 + \Delta x) - f(1)}{\Delta x}$$

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

Substitute for f(1) and f(1 + $\Delta x$) 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. Jul 15, 2010

Staff: Mentor

BTW, you should post calculus problems (like this one) in the Calculus & Beyond section.