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

Miscellaneous

Misc 1
Important

Misc 2

Misc 3

Misc 4

Misc 5

Misc 6 Important

Misc 7

Misc 8

Misc 9 Important

Misc 10

Misc 11

Misc 12

Misc 13

Misc 14

Misc 15

Misc 16

Misc 17 You are here

Misc 18

Misc 19

Misc 20

Misc 21

Misc 22

Misc 23

Misc 24 Important

Misc 25

Misc 26

Misc 27 Important

Misc 28 Important

Misc 29

Misc 30 Important

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.