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 you subtract
the power subtract one from the powers they have 5×3 x to the 3-1 okay to take a look
at this formula right here and then take a look at this hopefully can see that this is
'n ambitious and -1 because of this problem 'n is equal to 330 multiplied by fence three
have 15 X the second power this is an example that involves the incorporation of the constant
multiple rule and the power rule as you deal with more more complicated functions in calculus
you have to often differentiate a function by making use of multiple alright lets take
a look at Formula this is the sum and difference rule so it tells us that the derivative of
the sum or difference of two functions so the derivative of the sum or difference
function is equal to the derivative of the year function value adding a subtracting from
each other to the derivative of the first function U plus or minus the derivative of
the second function right to thatbasically what the sum and difference rule represents
alright so let's take a look at An exampleso this problem says one of the derivative of
x to the third plus 7X plus four to have a sum of three terms here so we apply the sum
and difference rule one that enables us to do is to take the derivative of the individual
terms that he added together here in this result by Skip Thompson steps so let's go
ahead and go over and after a quick sold the derivative of exited third you apply to power
rules out of three and subtract one from three have 3X square the derivative of 7X you factor
out seven from X and X the first power we apply to power the power of the excellent
first power you power don't want from X the 1-1 and I am 1-10 exited zero power is one
so you left with seven this differently differentiation of seven actions you want really cool trick
that you can memorize when you differentiate functions of this nature first-degree terms
all you have to do is drop the variable in the constant is always the all derivative
for example think about why cool annexes the areas of slope becomes that of other derivative
also also when you doing with mx anything of that nature the derivative of MX is just
and so in this case we have 7X think about seven at the slope and this is X to the derivative
of 7X27 of the shortcut they can always use one of the derivative for think about the
first really went over that is the all constant function will remember the derivative of a
constant is zero so you have any zeros here so I skipped a lot of sets deliberately to
challenge you if you don't understand is seeking to ship a private workout all the details
and you get 3X square seven citizen example of the sum and difference rule right next
to take a look at the product rule this to the data derivative of the product of two
functions you envy you what the answer is so the derivative of you envy is equal to
you the cry with them and what is going on here or private is another notation for representing
the derivative if you write an expression that involves taking a lot of derivatives
instead of writing DDX over and over again crime is a condensed way of expressing the
derivative so what is the direct DDX UB which is the same thing as UV prime is the you pry
loose UV prime as a think that seeing the time to derivative of you DDX of you lets
you time media company rightly see the benefit of the prime notation it helps simplify pages
of writing DDX sometimes that can be messy so using the prime notation can be very beneficial
to that the product will for you guys apply to an example DDX of express my next easy
to function here without the power function and the tree function site X so the function
of come second in the political order UV you come before the to function it comes on second
is the first function you apply a product rule have the second function times you prime
the derivative of the first plus you the first function times the derivative of the second
haven't done over the differentiation rules for tree functions on this stuff here just
to illustrate how the product rule can be by articulate The last set of formulas edited
of course you will so DDX of you over the BF versus function function in the numerator
you in the function of the denominator is the arrow the derivative of the exit your
the which is the thing that you were a private member primer presents the derivative is equal
to the you prime minus UV prime over the square I said that the portion rule there for you
so let's take a look at an example of the portion rule so we have the derivative of
exit for ln x equal to the exited on the function of the derivative of you you which is a numerator
function X minute you which is X on the derivative of the denominator ln x prime over the denominator
ln x where the result can a simplified further but since we haven't done over the derivative
of ln x natural logarithm of x yet I'm just finished up here I will be going over those
the derivative of ln x am in the upcoming installments and also another point to note
is that the denominator function cannot be zero I just wanted to in a mnemonic device
that some use to remember the portion rule personally don't really understand how beneficial
but a lot of students like it so I I can be good to share it to be in this mnemonic device
represents the derivative high represents the function on a top and low represents the
function of the bottom the top is use vitamin C so you say hi to me despite the stickier
so low which is the denominator function of the beehive the derivative of the numerator
function you prime minus high to the major functions you below the derivative of the
low of the function in the denominator the prime divided by low square which is where
so students disable the high minus tidy little over low square at how he remembered a portion
rule but I like this this format better the square I maybe you prime minus UV prime over
the square to whichever one helps you remember the portion rule that will be great always
make use of the Summit tutorial you can copy them down just made flashcards for yourself
and then you just flip through them over and over again and finish you to memorize all
you differentiation formulas at a particular time towards this presentation appreciated
the subscriber channels they can get updates to the remaining flashcards for remembering
the differentiation rules explicit comments let us know what you think about this presentation
in the derivative thumbs up if you like it and you also don't forget to share with your
friends more clips can be found on mathgotserved.com have indicated earlier thanks again for watching
and have a wonderful day