CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 13 – Limits and Derivatives Maths
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sin sin
cos x.cos
x a x x a
f ' x
2
cos x
cos x a x
2
cos x
cos a
2
cos x
Question 22:
Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s
are fixed non-zero constants and m and n are integers): x 4 (5 sin x - 3 cos x)
Solution 22:
4
Let f ( x) x (5sin x
3cos x)
By product rule,
4 d
d 4
f '( x) x (5sin x 3cos x) (5sin x 3cos x)
x
dx
dx
d d
d
x 5 sin x 3 cos x (5sin x 3cos x)
x
dx dx
dx
4 3
x 5cos x 3sin x (5sin x 3cos x) 4x
3
x 5xcos x 3xsin x 20sin x 12cos
x
4 4
Question 23:
Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s
are fixed non-zero constants and m and n are integers): (x 2 + 1) cos x
Solution 23:
Let f(x) = x
2
1 cos x
By product rule,
2 d
d 2
f ' x x 1 cos x cos x x 1
dx
dx
2
x 1 sin x cos x 2x
2
x sin x sin x 2xcos
x
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