[Boards: 3 / a / aco / adv / an / asp / b / biz / c / cgl / ck / cm / co / d / diy / e / fa / fit / g / gd / gif / h / hc / his / hm / hr / i / ic / int / jp / k / lgbt / lit / m / mlp / mu / n / news / o / out / p / po / pol / qa / r / r9k / s / s4s / sci / soc / sp / t / tg / toy / trash / trv / tv / u / v / vg / vp / vr / w / wg / wsg / wsr / x / y ] [Home]
4chanarchives logo
derivative
Images are sometimes not shown due to bandwidth/network limitations. Refreshing the page usually helps.

You are currently reading a thread in /wsr/ - Worksafe Requests

Thread replies: 4
Thread images: 1
File: 3.jpg (135 KB, 1600x900) Image search: [Google]
3.jpg
135 KB, 1600x900
can anyone give me the steps to find the derivative of this function y=x^(2-x) using the limit definition? pic unrelated
>>
y=2x-x^2
(h->0)lim(2(x+h)-(x+h)^2 - 2x + x^2)/h
=lim(2h - 2xh - h^2)/h
=lim(2 - 2x - h) = 2 - 2x

if you use y' = f'(x) = (h->0)lim(f(x+h) - f(x))/h
>>
>>40716
erm I misread it
y = exp((2-x)lnx)
so it will not be as easy
>>
>>40681
It's easier to write the function differently first:
x^(2-x) = e^ln(x^(2-x)) = e^((2-x)ln x)

Now you should be able to solve it using the derivatives of the exponential function and of the natural logarithm, the chain rule, and the product rule.

https://en.wikipedia.org/wiki/Derivative#Rules_of_computation

But perhaps you need a solution without using the known rules (limit definition).
Thread replies: 4
Thread images: 1

banner
banner
[Boards: 3 / a / aco / adv / an / asp / b / biz / c / cgl / ck / cm / co / d / diy / e / fa / fit / g / gd / gif / h / hc / his / hm / hr / i / ic / int / jp / k / lgbt / lit / m / mlp / mu / n / news / o / out / p / po / pol / qa / r / r9k / s / s4s / sci / soc / sp / t / tg / toy / trash / trv / tv / u / v / vg / vp / vr / w / wg / wsg / wsr / x / y] [Home]

All trademarks and copyrights on this page are owned by their respective parties. Images uploaded are the responsibility of the Poster. Comments are owned by the Poster.
If a post contains personal/copyrighted/illegal content you can contact me at [email protected] with that post and thread number and it will be removed as soon as possible.
DMCA Content Takedown via dmca.com
All images are hosted on imgur.com, send takedown notices to them.
This is a 4chan archive - all of the content originated from them. If you need IP information for a Poster - you need to contact them. This website shows only archived content.