Find the derivative of sinx . cosec x+ secx . cotx
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Answer:
(i) sin x cos x Let f(x) = sin x. cos x, which is product of two functions. So, formula of derivative of product of two functions. = – sin2 x + cos2 x = cos2 x – sin2 x = cos 2x (∵ cos2 x – sin2 x = cos2x) Hence, derivative of given function sin x cos x = cos 2x (ii) sec x Let f(x) = sec x [From the formula of derivative of quotient of two functions] Hence, derivative of the given function sec x = sec x tan x (iii) cosec x Let f(x) = cosec x Then, derivative of f(x) = – cosec x cot x Hence, derivative of the given function cosec x = – cosec x cot x (iv) 3 cot x + 5 cosec x Let f(x) = 3 cot x + 5 cosec x Hence, derivative of the given function 3 cot x + 5 cosec x is – 3 cosec2 x – 5 cosec x cot x (v) 5 sin x – 6 cos x + 7 Let f(x) = 5 sin x – 6 cos x + 7 Hence, derivative of the given function 5 sin x – 6 cos x + 7 is 5 cos x + 6 sin x.Read more on Sarthaks.com - https://www.sarthaks.com/738469/find-the-derivatives-of-the-following-i-sin-x-cos-x
Answer:
- cosecx.cotx Answers is currently