Calculus Cheat Sheet

Leave the English language at the door and study with me. Here is a summary of the last 5 weeks worth of calculus I learned.

The whole reason that we have math at all is to answer and solve problems. How fast will this tank fill up? When can we expect this car to be at top speed? Can I out run these cops? Calculus is derived from Issac Newton, God bless and damn his soul, because he wanted to solve problems in physics.

The matter that interested Newton was how to find the slope of a curved line, whether it be a parabola

The Relation of Rate, time, and quantity


Where r is rate, q is quantity, and t is time.

This is the bare bones of many different rate equations, including speed and acceleration.

The Equation of a Line



The Concept of Infinity

Infinity is a big number. It goes to the end of the universe, and back.

But infinity has limits. (Take that math puns.)

The Definition of a Derivative

Imagine if you have a curvy line on a graph:

The whole point of finding the derivative is to be able to tell the slope at any point on the curve. This derivative can be used to find the speed, velocity, acceleration, and rate of growth! As annoying as it is to learn, it’s very important in science fields for engineering and physics.


The Power Rule

This is the much simpler way of the definition of a derivation that comes down to pure memorization:

If f(x)=x^n

Then f'(x)=nx^n-1

The Product Rule

Once the


Trignomic Function Derivative
 sin x cos x
 cos x -sin x
 tan x  sec^2 x

There are a couple of helpful websites for your calculus homework!

Derivative Calculator – If you can handle ugly translation text, this is the website for you. I suggest trying the problem out for yourself and then checking it here. Have integrity, don’t cheat!

Simplify Calculator – Half of the issues in math is not understanding basic algebra. And much of higher tier math is taught in such a way that unless it’s simplified, there’s no way to answer it. Use this site wisely!

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