CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 13 – Limits and Derivatives Maths
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Question 21:
Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s
sin xa
are fixed non-zero constants and m and n are integers):
cos x
Solution 21:
sin xa
Let f(x) =
cos x
By quotient rule,
d
d
cos x sin x a sin x a
cos x
'
dx
f x
dx
2
cos x
d
cos x sin x a sin x a sin x
f ' x
dx
... i
2
cos x
Let g(x)=sin (x + a). Accordingly, g(x + h) = sin (x + h + a)
By first principle,
g( x h)
g x
g'
x
lim
h0
h
1
lim sin x h a sin x a
h0
h
1 x h a x a x h a x a
lim 2cos sin
h0
h
2
2
lim 1 2cos 2x 2a h sin h
h0
h
h
2
h
sin
2x 2a h
2
lim cos
h0
h
h
2
sin
h
2x 2a h
2
h
limcos .lim
As h 0 0
h0
h
h
0
h 2
2
2
2x
2a sinh
cos 1 lim 1
2
h0
h
cos x a ... ii
From (i) and (ii), we obtain
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