web analytics

Misc 24 - Find derivative: (ax2 + sin x) (p + q cos x) - Miscellaneous

Slide70.JPG

  1. Class 11
  2. Important Question for exams Class 11
Ask Download

Transcript

Misc 24 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): (ax2 + sin x)( p + q cos x) Let f (x) = (ax2 + sin x) (p + q cos x) Let u = ax2 + sin x & v = p + q cos x ∴ f(x) = uv So, f’(x) = 𝑢𝑣﷯﷮′﷯ Using product rule 𝑢𝑣﷯﷮′﷯= 𝑢﷮′﷯𝑣+ 𝑣﷮′﷯𝑢 Finding u’ & v’ u = ax2 + sin x u’ = (ax2 + sin x)’ = 2ax + cos x v = p + q cos x v’ = (p + q cos x)’ = 0 + q ( – sin x) = – q sin x Now, f’(x) = 𝑢𝑣﷯′ = 𝑢﷮′﷯𝑣+ 𝑣﷮′﷯𝑢 = (2ax + cos x) (p + q cos x) + ( – q sin x) (ax2 + sin x) = – q sin x (ax2 + sin x) + p + q cos x) (2as + cos x)

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
Jail