Last updated at May 29, 2018 by Teachoo

Transcript

Misc 17 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): sinx + cosx sinx − cosx Let f (x) = sinx + cosx sinx − cosx Let u = sin x + cos x & v = sin x – cos x ∴ f(x) = 𝑢𝑣 So, f’(x) = 𝑢𝑣′ Using quotient rule f’(x) = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 Finding u’ & v’ u = sin x + cos x u’ = (sin x + cos x)’ = (sin x)’ + (cos x)’ = cos x – sin x v = sin x – cos x v’= (sin x – cos x)’ = (sin x)’ – (cos x)’ = cos x – ( – sin x) = cos x + sin x Now, f’(x) = 𝑢𝑣′ = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 = ( cos𝑥 − sin𝑥) ( sin𝑥 − cos𝑥) − ( cos𝑥 + sin𝑥) ( sin𝑥 + cos𝑥) ( sinx −co𝑠 𝑥)2 = − ( sin𝑥 − cos𝑥) ( sin𝑥 − cos𝑥) − ( sin𝑥 + cos𝑥) ( sin𝑥 + cos𝑥) ( sinx − co𝑠 𝑥)2 = −( sinx − co𝑠 𝑥)2 − ( sinx + co𝑠 𝑥)2 ( sinx − co𝑠 𝑥)2 = − [( sin2𝑥 + cos2𝑥 − 2 sin𝑥 cos𝑥) + (𝑠𝑖𝑛2𝑥 + 𝑐𝑜𝑠2𝑥 + 2𝑠𝑖𝑛𝑥 cos𝑥)] ( sinx − co𝑠 𝑥)2 = − ( 2𝑠𝑖𝑛2𝑥 + 2𝑐𝑜𝑠2𝑥 − 0) ( sinx − co𝑠 𝑥)2 = −2 (𝒔𝒊𝒏𝟐𝒙 + 𝒄𝒐𝒔𝟐𝒙) ( sinx − co𝑠 𝑥)2 = −2 (𝟏) ( sinx − co𝑠 𝑥)2 = −𝟐 ( 𝒔𝒊𝒏𝐱 − 𝒄𝒐𝒔 𝒙)𝟐

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Misc 17 You are here

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.