Examples : Derivatives of Composite Functions (Using the Chain Rule) Video Lecture | Mathematics (Maths) Class 12 - JEE

hello friends this video on continuity
and differentiability part 17 is brought
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fear from exam before watching this
video please make sure that you have
watched part 1 to power 16 Hindus let us
see some examples of this
the first example say is sine X square
plus 5 so in this case if you know if
you see we know the derivative of sine X
we know the derivative of x squared is 5
both these we know right but we don't
want any video of sine expense and if
you see this is nothing but a composite
function this is if I assume this guy is
let suppose them V and this guy is U so
my function is V of you correct
you take you first and then find V of
this this becomes signs X square plus V
1 V of U where my V is sine X and U is X
square plus v so what I do here is I
assume X square plus 5 s e correct
I found DD by DX is nothing but events
why because if I assume sine square X
square minus T I get Y as sine P if I Y
is sine T I can get dy by DT here
so my dy by DT is nothing but cos T so I
have dy by DT I have DT by DX I can get
dy by DX my dy by DX is nothing but dy
by DT into DT by DX in both
exist in my case dy by DT exists cos T
DT by DX exists to X so this becomes cos
T in US and T is nothing but X square
plus five so this becomes cos of X
square plus 5 into to it and that is
masked see the more question you solve
the bitrate is just you watch this video
for the concepts worse I will recommend
you to solve as many cushions as you can
because the more cushion you saw the
better ISM is your speed and the
Maitland's concept in this question what
we did we had this sine X square plus
five formula and this was composite
function correct and this function again
we wrote as V and you form where we
become sine x and u becomes X square
plus 5 and then this guy was something
but V of you and what we did was we
assumed this guy has T so this becomes Y
became sine T because this is nothing
but Y and I got two equations right I
got two equation D is nothing but X
square plus five and Y is sine T correct
so from this equation I get DT by DX
because this equation is the term of T
in X this equation I get dy by DT
because this guy is in term of Y and D
you multiply both those you get dy by DX
let's take some more example because
chain will are tricky one here is if you
see this is a composite function cos of
sine X so in this case also we can
convert into know it suppose Y is equal
to COS of sine X so if I write into this
suppose Rho V and you form so my V
becomes let's suppose cos x and you
become sine X so my this this is FX my
FX is nothing but V of you you take you
first and then you take V so this is my
function
composite functions what I can do I can
write this AST
so I get to equation T is equal to sine
X and I get Y is equal to cost correct
this guy is in form of T and X so I can
get DT by DX from this guy and this guy
is VY and T I can get dy by DT and I
another formula I have to find give I by
DX or this particular equation which is
nothing but dy by DT into DT my delays
these two exist
let's find dy by DT first because dy by
DT is required here so if I take this
equation my dy by DT becomes 4 cos T the
depressions minus sine T so minus sine T
is my conceivabilities writer minus sine
T is my critique evaluate now I want D
DX DT by DX I'll take this equation so T
is equal to sine X so my DT by DX is
nothing but cos x so right cause
exceeded and that is Manship since T is
something not given in question I can
replace T with sine X this becomes minus
sine of
smile X and du constant and that does
violence so what I have done I just
observe that this is a composite
function since this guy has a complex
function I was able to write this in
this fashion V is going to cross excuse
me sine X and I just made sine X STI got
to equation and I know I can write dy by
DX s dy by DT DT by DX I got the value
of dy by DT I got the value of DT by DX
bar next let's take one more example
sine of AX plus very similar to the old
cushion chaos a QC we know ax plus B I
know how to differentiate I know how to
differentiate sine X so if I assume sine
X as Li and ax plus B as u then this guy
my FX which you can see here this guy is
nothing but we offer you please note it
is not u of V is V of you because sine X
come first and this guy
second if you are having issue in this
you can again wash my cross 11 video
where I explain how to do this and you
learn this in class 11 - so this is my
FX is going to be a few now if I might
take this guy is T why because it's
composite function again uses T so I got
to the equation T is equal to X plus B
and Y is you can do sine T Y because Y
is equal to sine X plus we know that I
am adding Y is equal to sine T now have
to write again I have to find d-y-by-dx
I can try this dy by DT DT by DX Y
because composite function and chain
rule is true for this divided by reading
you can leave ability after you the
situation because this equation is then
comes of Y and T so Y is equal to sine t
dy by DT will becomes cos T this the
relation we have done so this becomes
cos T into this equation I have T is
equal to ax plus B so I get DT by DX is
nothing but into differentiate X with
respect to X you get 1 and differentiate
V with respect to X is 0 because any
constant if the script to 0 becomes 0 so
this becomes a this is a a cos T is my
answer busty is not in the question so I
will replace t ax plus B so I'll get cos
of a plus B into and that is - I can
write this as a cos it's a fancier way
to write that is very simple so what we
observe in these questions are resolved
portions where we have a composite
function and I can use chain rule thank
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