Ex 13.2, 11 - Find derivative: (i) sin x cos x (ii) sec x - Derivatives by formula - other trignometric

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  1. Chapter 13 Class 11 Limits and Derivatives
  2. Serial order wise
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Ex 13.2, 11 Find the derivative of the following functions: (i) sin x cos x Let f (x) = sin x cos x. Let u = sin x & v = cos x f(x) = uv So, f (x) = (uv) = u v + v u Here, u = sin x So, u = cos x & v = cos x So, v = sin x Now, f (x) = (uv) = u v + v u = cos x . cos x + ( sin x) sin x = cos2x sin2x = cos 2x Hence f (x) = cos 2x Ex13.2, 11 Find the derivative of the following functions: (ii) sec x Let f (x) = sec x f(x) = 1 cos Let u = 1 & v = cos x So, f(x) = f (x) = using quotient rule f (x)= 2 Finding u & v u = 1 u = 0 & v = cos x v = sin x Now, f (x) = = 2 = 0( cos ) ( sin ) (1) 2 = 0 + sin 2 = sin 2 = sin cos . 1 cos = tan x . sec x Hence f (x) = tan x . sec x Ex13.2, 11 Find the derivative of the following functions: (iii) 5 sec x + 4 cos x Let f (x) = 5 sec x + 4 cos x. Now, f (x) = ( 5 sec x + 4 cos x) = (5 sec x) + (4 cos x) = 5 (sec x . tan x) + 4 ( sin x) = 5 sec x . tan x 4 sin x Ex 13.2, 11 Find the derivative of the following functions: (iv) cosec x Let f (x) = cosec x f(x) = 1 sin Let u = 1 & v = sin x f(x) = So, f (x) = Using quotient rule f (x) = 2 Finding u & v u = 1 u = 0 & v = sin x v = cos x Now, f (x) = = 2 = 0 ( sin ) cos (1) 2 = 0 2 = 2 = sin . 1 sin = cot x cosec x = cosec x cot x Hence f (x) = cosec x cot x Ex13.2, 11 Find the derivative of the following functions: (v) f (x) = 3cot x + 5cosec x. Given f (x) = 3cot x + 5cosec x Now, f (x) = (3cot x + 5cosec x) = 3(cot x) + 5( cosec x) = 3cosec2x 5 cot x cosec x = 3 cosec2x 5 cosec x cot x Ex13.2, 11 Find the derivative of the following functions: (vi) f (x) = 5sin x 6 cos x + 7. Let f (x) = 5sin x 6cos x + 7 f (x) = (5 sin x 6 cos x + 7) = (5 sin x) (6 cos x) + (7) = 5 cos x 6 ( sin x ) + 0 = 5 cos x + 6 sin x Ex13.2, 11 Find the derivative of the following functions: (vii) f (x) = 2 tan x 7 sec x f (x) = 2 tan x 7 sec x. Now, f (x) = (2 tan x 7 sec x) = (2tan x) (7sec x) = 2 (tan x) 7 (sec x) = 2 sec2 x 7 (sec x tan x) = 2 sec2 x 7 sec x tan x

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