web analytics

Misc 17 - Find derivative: sin x + cos x / sin x - cos x - Derivatives by formula - sin & cos

Slide52.JPG
Slide53.JPG

  1. Chapter 13 Class 11 Limits and Derivatives
  2. Serial order wise
Ask Download

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): sin﷮x + cos﷮x﷯﷯﷮ sin﷮x − cos﷮x﷯﷯﷯ Let f (x) = sin﷮x + cos﷮x﷯﷯﷮ sin﷮x − cos﷮x﷯﷯﷯ Let u = sin x + cos x & v = sin x – cos x ∴ f(x) = 𝑢﷮𝑣﷯ So, f’(x) = 𝑢﷮𝑣﷯﷯﷮′﷯ Using quotient rule f’(x) = 𝑢﷮′﷯𝑣 − 𝑣﷮′﷯𝑢﷮ 𝑣﷮2﷯﷯ 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) = 𝑢﷮𝑣﷯﷯﷮′﷯ = 𝑢﷮′﷯𝑣 − 𝑣﷮′﷯𝑢﷮ 𝑣﷮2﷯﷯ = ( cos﷮𝑥 − sin﷮𝑥) ( sin﷮𝑥 − cos﷮𝑥) − ( cos﷮𝑥 + sin﷮𝑥) ( sin﷮𝑥 + cos﷮𝑥)﷯﷯﷯﷯﷯﷯﷯﷯﷮ ( sin﷮x −co𝑠 𝑥﷯)﷮2﷯﷯ = − ( sin﷮𝑥 − cos﷮𝑥) ( sin﷮𝑥 − cos﷮𝑥) − ( sin﷮𝑥 + cos﷮𝑥) ( sin﷮𝑥 + cos﷮𝑥)﷯﷯﷯﷯﷯﷯﷯﷯﷮ ( sin﷮x − co𝑠 𝑥﷯)﷮2﷯﷯ = −( sin﷮x − co𝑠 𝑥﷯)﷮2﷯ − ( sin﷮x + co𝑠 𝑥﷯)﷮2﷯﷮ ( sin﷮x − co𝑠 𝑥﷯)﷮2﷯﷯ = − [( sin2﷮𝑥 + cos2﷮𝑥 − 2 sin﷮𝑥 cos﷮𝑥) + (𝑠𝑖𝑛2𝑥 + 𝑐𝑜𝑠2𝑥 + 2𝑠𝑖𝑛𝑥 cos﷮𝑥)]﷯﷯﷯﷯﷯﷮ ( sin﷮x − co𝑠 𝑥﷯)﷮2﷯﷯ = − ( 2𝑠𝑖𝑛2𝑥 + 2𝑐𝑜𝑠2𝑥 − 0)﷮ ( sin﷮x − co𝑠 𝑥﷯)﷮2﷯﷯ = −2 (𝒔𝒊𝒏𝟐𝒙 + 𝒄𝒐𝒔𝟐𝒙)﷮ ( sin﷮x − co𝑠 𝑥﷯)﷮2﷯﷯ = −2 (𝟏)﷮ ( sin﷮x − co𝑠 𝑥﷯)﷮2﷯﷯ = −𝟐 ﷮ ( 𝒔𝒊𝒏﷮𝐱 − 𝒄𝒐𝒔 𝒙﷯)﷮𝟐﷯﷯

About the Author

CA Maninder Singh's photo - Expert in Practical Accounts, Taxation and Efiling
CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .
Jail