<![CDATA[Hello, I'm Sahib. - Blog]]>Tue, 08 Mar 2016 16:53:08 -0800Weebly<![CDATA[My public key!]]>Sat, 27 Feb 2016 19:33:18 GMThttp://mistersahib.weebly.com/blog/my-public-key-----BEGIN PGP PUBLIC KEY BLOCK-----
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<![CDATA[Hurray for derivatives!]]>Sat, 21 Nov 2015 03:17:12 GMThttp://mistersahib.weebly.com/blog/hurray-for-derivativesAbout the time you go into college, you are thrown into a brand new field of mathematics, one that most people seem to have a trouble grasping: calculus.
Calculus is my favorite part of mathematics. Sure, algebra is a close-second (<3 linear equations), but calculus just rips algebra to shreds.
One reason for this is that calculus introduces a quirky new concept: derivatives.

Derivatives are (taken from Wikipedia):
"The derivative of a function f(x) of a variable x is a measure of the rate at which the value of the function changes with respect to the change of the variable."
Most people learn derivatives with the boring "actual definition", but I learned derivatives (and pretty much all of calculus) with just rules.
d/dx(c)=0
Now, let me break this down for you:
d/dx is the derivative operator. It tells you "Hey! You should take the derivative of this!" (note that it is written as d over dx (d on top of dx with a line between them))
(c) tells us that we want to take the derivative of c. In this case, c represents any constant.
=0.... do I have to explain this?
You may be asking, why is it 0?
Well, calculus is the study of change.
Derivatives are the rate of change with respect to a variable.
c is a constant, which means it doesn't change.
All numbers (1, 3, -8, 3.14159...) that have a value that doesn't change are constants.
Since the derivative is the rate of change, and c never changes, the rate of change is 0.
Here's another one:
d/dx(x)=1
Now, this is telling us that the derivative of x (with respect to x) equals 1. Why is this?
Well, you could represent x as 1x.
1x is the same as 1 * x.
Since it's being multiplied by 1, we could say that the rate of change is 1.
Similarly:
d/dx(nx)=n
This states that the derivative of nx (with respect to x) is n.
This is because nx represents n times x.
Since we are changing x by multiplying it by n, n is the derivative.
Yes, it is confusing, but eventually you'll get the hang of it
d/dx(x/y) = {[y * d/dx(x)] - [x * d/dx(y)]} / y^2
Now this, this is confusing. But it's even more confusing when I put it into words
"The derivative of x over y is y times the derivative of x, minus x times the derivative of y, all over y squared."
Let me give you a demonstration.
d/dx(3x^2/5x) = [(5x * 6x) - (3x^2 * 5)] / 5x^2
Quickly, here are some other rules:
d/dx(x^n)=nx^n-1
d/dx(1/x)=ln(x)
d/dx(x + y) = d/dx(x) + d/dx(y)
'
And that's all I have for this blog post. Goodbye

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