Sorry - more stuff i don't even know where to begin on

[scrum]

*sigh*

I have no idea how to approach this. I know the product and quotient and chain rule and thats it. even just telling me what rule to google to get it will be a great help as i have all night to do these.

thanks.

 

[jwpaine]

This is conceptual not computational.

What is the function being differentiated, at what point (a) is it being differentiated?

Ie: for what function f(x) and value a, does the difference quotient \(\displaystyle \L \lim _{h\to\0} \frac{f(a + h) - f(a)}{h}\) give you \(\displaystyle \L \lim_{h\to\0} \,\,\,\, \frac{(1 + h)^{10} - 1}{h}\,?\)

 

[galactus]

If we evaluate the limit, we find it is 10.

Let u=1+h:

Therefore, \(\displaystyle \L\\\lim_{u\to\1}\frac{u^{10}-1}{u-1}\)

Expanding, we get:

\(\displaystyle \L\\\sum_{k=0}^{9}u^{k}\)

If u=1, then we have the limit as 10.

So, the derivative of said function is 10.

There's another clue.