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Differentiation Derivatives Flash Cards Pt I Memorize Fast Calculus AB

good day students welcome to part one of our differentiation flashcards were going to be going over formulas 136 and this am review installment more clips can be found mathgotserved.com for AP calculus students you cannot go to a mathgotserved.com under ap calculus to gain access a wide variety of great tutorial to go ahead and take a look at the first formula now before we start out like to go over some critical components of this five of these flashcards so that you can basically know your orientation where i position certain things on the upper left upper left corner is the name of the function that was going to be learning the differentiation formula for on the upper right corner we have the orientation of the card into the front or the back and in on the lower right corner you how the number assigned to these index card

okay for this for these flashcards I'm going over the going to be going fromflash card 1 all the way to 6 among the first formula were going to do with the constant function it says ddx of C to DDX is basically a notation one of the notation for differentiation so the way you read this is also provided below you see here it says read the its read is is the derivative of constants of DDX is reported represent an operation the differentiation process so this front of his part is asking you the derivative DDX of the constant C is what so thats how you read it can't and answered on the reverse is that the card for the derivative of the constant functions the is equal to zero Manuals also be providing examples on the reverse side of each index card to help you associate the formula without concrete situation for example let's take a look at an example of the case that represents the constant function differentiation will for example is DDX of pi we know that pi is a constant is an irrational number so qualifies as C so this example helps us to see that the derivative DDX of pi is equal to zero articulate The next formula this is the constant multiple formula number two so it says DDX OC times F of X so what is normal basically represented the derivative of the constant multiplied by function what is the derivative a constant multiplied by a function to the derivative of the constant multiplied by function is equal to C times is DDX out of the so what this formulas, in essence is that he constant multiple of the function can be factored out from the argument that you differentiating on the left side you can on you differentiate his entire expression C times the function were see the constant because the multiple rule tells you that that's can be factored out and they just focus on differentiate in the function using whatever differentiation rule you want to apply right so that's the main idea in the let's take a look at an example what is a derivative of three times tan x his situation tan x is the function and three is the constancy so this example helps us to see that it's the same thing as three multiplied by the derivative of tan x in the upcoming installment I will be going over what the derivative of trig functions are that's that's simplify this all the way because we do not know what the derivative of tan or so just remember the constant multiple rule gives you the rights to factor out constant that are being multiplied with function before you differentiate and out the differentiation of course do not forget to multiply the constants a factor out your derivative to take a look at formula number three formula 3 is the power rule So what is a power rule the power rule tells us that the derivative X raised to the nth power the derivative of x raised to the nth power for the answer the derivative of x raised to the nth power is equal to 'n times X raised to the n and -1 right so basically take the power power down multiply the function but you reduce the power of the term that had power regionally by one so and X to the end -1 is the derivative of X to the end power Let's take a look at an example here the question is what is the derivative of 5X to the third power now to find the derivative I made use of one of the formulas that we covered for which is the constant multiple rule begin see it in action here because I factored out the five and then I focused on differentiating this power function right here x to the third outline of powerful to X the third what am I supposed to do high-powered others exponents of this three come down here you have it has 5×3 and then

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