The long way to take a derivative is pointless. Every teacher teaches it first, but then they will teach you the easy way. The easy way takes about a tenth of the time and is very easy.
How to Take a Derivative the Easy Way
The formula to take the derivative is n(x)n-1, but this is how you do it. First all you do is take the exponent and put it out front of the equation, and then you subtract the exponent by 1. Yep that’s all there is to it (until you get to more complicated functions).
Here are some examples.
Ex. 5x3 first you take the 3 from five x cubed and place it in front. Then you subtract 1 from the exponent. This leaves you with 15x2. That’s the answer.
If you have something like 7x or anything with x to the first power, when you take the derivative, you are left with just the numeral in the front. So in this case just 7.
If there is no variable on the equation, the answer is 0. Anytime the equation is a constant, the answer is 0.
More complicated stuff
When running into more difficult problems like X1/4 always start by putting x to a power (so if the equation is the square root of x, just make it x1/2). After this, just follow the steps above. First, put the ¼ to the front. Then, subtract one. You will be left with ¼ X-3/4. So your answer is 1/4x3/4.
When addition or subtraction is involved, you must do the derivative of each monomial separate. So in the example x9 -2x, your answer would be 9x8-2.
Derivative of e. The derivative of ex is just ex. This gets more complicated when you take the derivative of something like e3x. When doing this, you have to take the chain rule.
These don’t really follow a rule, you just kinda have to learn these. Here is a list of the answers to the following triganomic functions.
Derivative of Sin(x)=cos(x)
Derivative of cos(x)=-sin(x)
Derivative of tan(x)=sec2(x)
Derivative of csc(x)=-csc cot
Derivative of sec(x)=sec tan
Derivative of cot(X)=-csc2x
When you have something complicated such as 4(X²+3)2, you have to do the chain rule. The chain rule is not hard, but easy to skip steps when rushing through problems.