How to do Derivatives

What is a derivativeA derivative is in a branch of Mathematics called Calculus. The derivative is the measure of how a function changes as its input changes. It tells what the slope is at any point on a graph as well. It is one of the two properties of single variable calculus.Back to Index

Why it is ImportantThe importance of the derivatives is vital for the world today. Derivatives can tell such things like how fast some one was going, the acceleration they were experiencing, and where they were with just one equation. It also gave us the a way to prove all of the volume equations in the world.Back to Index

Notations of DerivativesThere many ways to see the same notation for derivatives. Great mathematical minds used different ways to say the same thing. In class we will use Leibniz notation.This means that dy/dx is the notation for a derivativeFor multiple derviatives there is a power to d so for example the second derivative would be written as d2y/dx2Back to Index

Difference QuotientThe difference quotient is what is formally used to find a derivative. The difference quotient is a math equation that finds the limit as x approaches a certain x value. The difference quotient is shown below.An example of difference quotientBack to Index

Constant and Power RuleThe constant rule is used as an informal way to find the derivative. The constant rule says that any constant number when taking the derivative of it equals 0For instance the derivative of 5 = 0The power rule is a short cut to find derivatives quick and easy. The rule states that you take the exponent of any number and multiply it by the number and subtract one from the exponent itself.Some examplesBack to Index

Sum/Difference RuleThe sum and difference rule are another informal way of finding a derivative. The sum and difference rule states that you can break up any equation by a plus or minus sign to find the derivative.For instance x2+5 could be broken up to be d/dx x2 + d/dx 5Back to Index

Quotient RuleThe quotient rule is also an informal way to find the derivative. It is used when to functions are divided togetherFor instance (x2 + 5)/(x+4) is two functions that would be perfect for the quotient ruleThe quotient rule is (g(x)fI(x) f(x)gI(x)) / (g(x))2Back to Index

Chain RuleThe chain rule is the Golden Rule. It is the rule to rule all rules. The chain rule states that for any function inside another function you take the derivative of the inside function and multiply it by the derivative of the outside functionFor instance find d/dx of (x2 + 5x2 )2The chain rule is Back to Index

Trigonometric FunctionsYou can take the derivative of trigonometric functions. They are always continuous and follow a pattern. This the pattern that you follow for trig functions d/dx sin(x)= cos(x) d/dx cos(x)= -sin(x) d/dx tan(x)= sec2 (x) d/dx csc(x)= -csc(x)cot(x) d/dx sec(x)= sec(x)tan(x) d/dx cot(x)= -csc2(x)Back to Index

Lets Take a QuizClick here to begin QuizBack to Index

null32052.51