Algebra of Derivative of Functions Video Lecture | Crash Course for MAT

hello friends my name is Samantha so
students in this lecture we will discuss
about algebra derivative of functions
okay so there is one theorem in which we
will discuss about different derivative
of sum of two functions derivative of
some difference of two functions
derivatives of product of two functions
as division of two functions
okay so I am writing here one by one it
is derivative of sum of two functions
okay so what the derivative is also
written as this origin synthesis this
okay so it is written as d by D H of G X
plus F X so now I can write it down
write it down separately so this is the
beauty of this operator which you can
separate the two functions and then
differentiate it separately and then it
is a case in derivative of difference of
two functions okay so it is also same as
the addition
B by D H F X minus D by DX DX okay so
this is equals to the means the
difference the differentiation of the
difference of the two function is equal
to the difference of the differentiation
of each function separately okay now I
am writing down the product of D by D a
effects into G H so here product rule
will get apply this is equal to G H D by
DX of effects okay
outside differentiation of first
function then effects outside D by D
itself GX
okay so this is the formula to find out
the dispensation of product of two
functions okay now I am writing here D
by DX of effects upon G a okay students
the formula is in the denominator part G
of X square and in liberators G of X
into D by DA FX minus FX d by DX of GX
okay
so this is the formula to find out the
destination of division of two functions
okay now we will discuss some questions
based on these okay so student here is
the question in which we need to find
out the derivative of FX which is equal
to x plus 1 upon X so this is equal like
Yubari formula in which I will write the
derivative of function this means D by D
FX by DX
equal to upon a d square V you - - you
be - this is the formula me to apply
where V is X so this is X square be as
it is definition of U is 1 minus u as it
is this is also 1 so X minus X plus 1
upon its quill so what I am getting here
student it is minus 1 by X square so the
differentiation of this function is
minus 1 by X square now let us do one
more question on trigonometric functions
find derivatives of effect that is equal
to sine square X okay so our function
given to us as sine square X so how the
solution goes for this is I need to find
out D of effect by DA which is equal to
D by DX I can write split sign it twice
so now here I will use the product rule
means the first function as it is sine X
hati's and differentiation of posit sine
X is POSIX and we have find out plus
other sine X as it is and cosines okay
so it is 2 sine X cosine which is equal
to sine of 2 X okay so this is the
derivative of this trigonometric
functions okay so now here I am writing
some important derivatives
okay so deep ideas of sine X equal POSIX
D by DX of Hosts is equals minus sine X
D by DX of NX equal secant squared X
okay and for some polynomial fencing
student but we need to do if D by DX of
X to power n is given but we will do
power will come in front and one power
is getting me n times X to power n minus
1 is the derivative of but and so for
example let's say I need to find out D
by DX of its square so R will become
forward and from power one be less so 2
minus 1 is 2x so what I am getting here
is the derivative of X square e to work
2 times X so I hope that now you are
pretty clear about all the questions are
but we have discussed in the end has
later and if you are still set in any
issue in any questions of limits and
derivatives chapter then please please
do comment in the comment section
student I will be more than happy to
help you guys there Thank You students
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