# Misc 3

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Misc 3 (Method 1) 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): (px + q) rx+s Let f(x) = (px + q) rx+s = (px + q) (rx –1 + s) Let u = (px + q) & v = (rx-1 + s) ∴ f(x) = uv So, f’(x) = (uv)’ f’(x) = u’v + v’u Finding u’ & v’ u = px + q u’ = p 1 . x1-1 + 0 = px0 = p v = rx – 1 + s v’ = r( – 1) x1 – 1 + 0 = – rx – 2 = − 𝑟 𝑥2 Now , f’(x) = (uv)’ = u’v + v’u = p(rx – 1 + s) + − 𝑟 𝑥2 (px + q) = p 𝑟𝑥+𝑠 − 𝑟 𝑥2 (px + q) = 𝑝𝑟𝑥 + ps − 𝑝𝑟 𝑥 𝑥2 – 𝑟𝑞 𝑥2 = 𝑝𝑟𝑥 – 𝑝𝑟𝑥 + ps – 𝑟𝑞 𝑥2 = 0 + ps – 𝑟𝑞 𝑥2 = ps – 𝑟𝑞 𝑥2 Hence, f’(x) = ps – 𝒒𝒓 𝒙𝟐 Misc 3 (Method 2) 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): (px + q) rx+s Let f(x) = (px + q) rx+s = px rx+s + q rx+s = px rx + px (s) + q rx + qs = pr + pxs + qrx + qs = pxs + qrx-1 + qs + ps Now, So, f’(x) = pxs + qrx−1 + qs + ps′ = (pxs)’ + (qrx-1)’ + (qs)’ + (ps)’ = ps . (1 . x1–1 ) + qr (-1 . x – 1 –1) + 0 + 0 = ps (x0) + qr ( -1 x-2) = ps (1) – qr x –2 = ps – 𝑞 𝑟 𝑥2 Hence f’(x) = ps – 𝑞𝑟 𝑥2

Misc 1
Important

Misc 2

Misc 3 You are here

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

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

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 .