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Misc 14 - Find derivative: sin (x + a) - Class 11 CBSE NCERT - Derivatives by formula - sin & cos

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  1. Chapter 13 Class 11 Limits and Derivatives
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Misc 14 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): sin (x + a) Let f(x) = sin (x + a) = sin x . cos a + cos x . sin a = cos a (sin x) + sin a (cos x) So, f’(x) = (cos a (sin x) + sin a (cos x))’ = (cos a (sin x))’ + (sin a (cos x))’ = cos a (sin x)’ + sin a (cos x)’ = cos a cos x + sin a ( – sin x) = cos a cos x – sin a sin x = cos a cos x – sin a sin x = cos (a + x) = cos (x + a) Hence f’(x) = cos (x + a)

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