4 min read•december 17, 2021
So, chances are that you've either started looking at what you need to know for AP Calc to get a head start or you're starting the class and you're completely lost. Fear not, this'll go through the basics and everything you need to know about derivatives!
Check out 🎥 Introduction to Finding Derivatives for more information!
Let's start off with a simple question: What is a derivative?
A derivative is the instantaneous rate of change of a function or slope of a tangent line on a graph, usually denoted by 'd/dx {f(x)}'
With taking a derivative, there are a couple of rules that you'll need to know
With this formula, 'x' is the variable, and 'n' is the exponent
Let's go over a quick example then:
We can see that the we have an exponent of two and a coefficient of 3.
Last but not least, we have to subtract one from the exponent value
And voila! You've taken a derivative using the power rule!
This rule is pretty straight forward and is used when you're taken a derivative of a function that has multiple terms.
The first one shows the sum rule while the second one shows the difference rule (That apostrophe means 'the derivative of')
This looks super confusing but the saying my teacher taught me really helped: "first times the derivative of the second plus second times the derivative of the first"
This can get pretty confusing through just words so we'll go over a quick example to help see how it should be done!
This first step is to identify our terms. We have 'x^2' and 'e^x' and we can see that they are being multiplied by each other. Now, we'll assume that 'x^2' is going to be our 'first' and 'e^x' is going to be 'second'
Now, we have to follow through with the formula and saying: "first times the derivative of the second plus second times the derivative of the first"
Just like the product rule, this one's a little bit of a doozy and so my teacher taught us a song to help remember this (it's meant to go with the Snow White and the Seven Dwarfs HeIgh-Ho song): "You take the low, d hi, minus the high, d low, square the bottom and away we go, heigh-ho, heigh-ho!"
This rule is more about identifying when you should use it and following the formula.
Want some more help on these rules, check out this video replay about the 🎥 Product and Quotient Rules.
Last but not least, we have chain rule. This is definitely the one that most people have the hardest time with so it's important that you can get the basics of it first.
We know how to take the derivative of this (power rule!) so we have the first part of this problem done
The last step is to multiply these two parts together
And that's it! These were the basic rules for taking a derivative that you'll need to know in order to get that five! If you need some additional practice, check out the resources linked below!
4 min read•december 17, 2021
So, chances are that you've either started looking at what you need to know for AP Calc to get a head start or you're starting the class and you're completely lost. Fear not, this'll go through the basics and everything you need to know about derivatives!
Check out 🎥 Introduction to Finding Derivatives for more information!
Let's start off with a simple question: What is a derivative?
A derivative is the instantaneous rate of change of a function or slope of a tangent line on a graph, usually denoted by 'd/dx {f(x)}'
With taking a derivative, there are a couple of rules that you'll need to know
With this formula, 'x' is the variable, and 'n' is the exponent
Let's go over a quick example then:
We can see that the we have an exponent of two and a coefficient of 3.
Last but not least, we have to subtract one from the exponent value
And voila! You've taken a derivative using the power rule!
This rule is pretty straight forward and is used when you're taken a derivative of a function that has multiple terms.
The first one shows the sum rule while the second one shows the difference rule (That apostrophe means 'the derivative of')
This looks super confusing but the saying my teacher taught me really helped: "first times the derivative of the second plus second times the derivative of the first"
This can get pretty confusing through just words so we'll go over a quick example to help see how it should be done!
This first step is to identify our terms. We have 'x^2' and 'e^x' and we can see that they are being multiplied by each other. Now, we'll assume that 'x^2' is going to be our 'first' and 'e^x' is going to be 'second'
Now, we have to follow through with the formula and saying: "first times the derivative of the second plus second times the derivative of the first"
Just like the product rule, this one's a little bit of a doozy and so my teacher taught us a song to help remember this (it's meant to go with the Snow White and the Seven Dwarfs HeIgh-Ho song): "You take the low, d hi, minus the high, d low, square the bottom and away we go, heigh-ho, heigh-ho!"
This rule is more about identifying when you should use it and following the formula.
Want some more help on these rules, check out this video replay about the 🎥 Product and Quotient Rules.
Last but not least, we have chain rule. This is definitely the one that most people have the hardest time with so it's important that you can get the basics of it first.
We know how to take the derivative of this (power rule!) so we have the first part of this problem done
The last step is to multiply these two parts together
And that's it! These were the basic rules for taking a derivative that you'll need to know in order to get that five! If you need some additional practice, check out the resources linked below!
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