Let’s Do Math. How to do Derivatives. By Niko Surace For kids in Calculus Subject: Mathematics Go to index. What is a derivative Why it is Important Notations of Derivatives Differentiation (Difference Quotient) Constant and Power Rule Sum/Difference Rule Product Rule Quotient Rule
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A 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.
The 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.
There 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.
The 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.
The 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 0
The 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.
The Product Rule is another informal way to do derivatives. The product rule as the name implies is used when taking the derivative of two things that are being multiplied together
The quotient rule is also an informal way to find the derivative. It is used when to functions are divided together
The 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 function
You can take the derivative of trigonometric functions. They are always continuous and follow a pattern. This the pattern that you follow for trig functions
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