How do you find the derivative of $x^{2/5}$ using the definition of the derivative?
I have a question that is highly similar to this one:  However, I'm not sure how to do this when fractional powers are involved. I understand that the answer involving the binomial theorem shows this for fractions too, but I'm not sure how to go through the mechanics of it all. For example, when trying to differentiate $\sqrt{ax+b}$, I get to   $$ \lim_{h \rightarrow 0}  \frac{\sqrt{a(x+h)+b} - \sqrt{ax+b}}{h} $$  then can't get the $h$ to cancel out. I think this involves algebraic manipulation of some sort, but can't figure it out.  Thanks
How to save animation as a video format I am basically trying to make an intro for my youtube channel. I am sort of familiar with the program because I was playing around with it for a long time, getting the basics of it. With the help of youtube videos I am basically done with my project. I put my name in it and everything. I just need to know how to save the animation onto my desktop as a file that I could open and would be in a video format. How to text-to-speech output using command-line? How to get speech output from entered text by using command-line?  Also facility to change speech rate, pitch, volume etc using simple command. Determine resultant velocity of an elastic particle-particle collision in 3d space So I have two particles that have collided in 3 dimensional space. I want the particles to rebound off of each other in an elastic manner. How do I determine the resultant velocity vector if I know: Both particles' initial velocity vector, their masses, and their initial position vectors relative to the origin.  I tried to follow the instructions on  but I am not sure how to make their equations work without polar coordinates / how to translate my data to polar coordinates.  Also, if you answer my question in terms of polar coordinates, can you explain which angle is theta and which is phi? Since there are 2 different conventions, I am not really sure which angle is being referred to in the explanation on the aforementioned website.  EDIT: This isn't for a class. I'm writing a physics engine for a gravity simulation I am making using Unity. I haven't taken kinematics since I was in high school, which is why I am so rusty. What is serial voting and how does it affect me? Seeing strange things in light I have noticed that if you look directly at tubelight (I have only white ones in my home) and close your eyes little, you see little random shaped colourless things sometimes with slow speed and sometimes with falling down.   They are shaped like circles with something in between and in chains of random length.   My father has also seen them. So, I am sure I am not imagining things. What the hell are they? How can I visualize the file system usage on Windows? Do we know how Senju Hashirama died? Canonical has recently announced , which is Ubuntu with a specific interface for mobile devices.  Where can I get phones with this version of Ubuntu pre-installed? If no devices are available yet, where can I pre-order one? Integration of elementary rational fractions $$\int{\frac{Mx+N}{x^2+px+q}}dx$$  When all the coefficients are given, it can be easily solved using substitution but I have no idea how to find a solution in a standard form.  What are the first steps? Does Time Machine backup programs like Photoshop and iWork? Remotely changing hard drive boot order, windows 7 I have one workstation chassis with two hard drives.  Depending on which one I boot from, I get one of two different operating systems: both are windows 7, but they have different static IPs, serve totally different purposes, etc.    The workstation has a modern asus motherboard, core i7 intel CPU, 32 GB ram.   Is there a way to remotely change which hard drive is booted from on a reboot?  Both systems have remote users, and i'd like a solution that is more elegant than being physically present and selecting boot order manually. C# - how can I get owner's name for a Mutex I have a shared mutex between 2 applications. I want to create an administration console that shows the current owner's name of the mutex.  How can I get the application name that currently owns the Mutex? Entity Framework and SQL Server View Indirectly access environment variable Given I have in a bash script  ev=USER   How can I get the environment variable value for $USER using ev?  Tried naively doing:  echo ${"$"$ev}   which results in bad substitution.  I'd expect to get back whatever the value of $USER is. After Hoth, why did Vader pursue the Millennium Falcon instead of Luke's X-Wing? In The Empire Strikes Back film, the opening crawl says:     The evil lord Darth Vader, obsessed with finding young Skywalker, has dispatched thousands of remote probes into the far reaches of space....   It has also been established in Return of the Jedi that Force users can sense each other:     Chewie whines nervously. Luke stares at the Huge Super Star Destroyer    that looms ever larger before them.      LUKE: Vader's on that ship.   If Darth Vader is obsessed with finding Luke and he can sense his presence, the obvious thing to do would be to follow Luke's X-Wing after the battle of Hoth rather than the Millennium Falcon. Why didn't he? Getting from Denver Amtrak to Fort Collins The eastbound Amtrak arrives Denver 6:38 PM (18:38).  How can I get to Fort Collins from there?   The  runs  from Denver International Airport to Fort Collins, but the airport is 40 km from the Amtrak station, so that's a major detour, that would mean taking bus FX from Market Street Station 7:18 PM, arriving at the airport at 8:27 PM, then the super shuttle 9:05 PM, arriving Fort Collins CSU at 10:55 PM; almost 4 hours after departing from Denver. Greyhound Lines appears to have a bus departing 12:45 AM, arriving 02:00 AM — although probably as quick as it gets, this is not exactly a comfortable time. RTD Denver has transportation to Longmont and  from Longmont to Fort Collins, but  appears to depart 7:05 PM — so I won't make it there when arriving by Amtrak.  A taxi would cost an estimated .   Is there any other way to get to Fort Collins when arriving by the eastbound Amtrak, any way that I've missed? Why Normality assumption in linear regression Mean, Average and Expectation What is the precise difference between the Mean, Average and Expectation ? Is there any mathematical formaulation to show the difference ? I see that often they are used interchangeably. Why am I not getting a java.util.ConcurrentModificationException in this example? Xcode - How to fix 'NSUnknownKeyException', reason: … this class is not key value coding-compliant for the key X" error?