Misc 6 - Chapter 12 Class 11 Limits and Derivatives
Last updated at April 16, 2024 by Teachoo
Derivatives by formula - x^n formula
Derivatives by formula - x^n formula
Last updated at April 16, 2024 by Teachoo
Misc 6 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): (1 + 1/š„)/(1 ā 1/š„) Let f(x) = (1 + 1/š„)/(1 ā 1/š„) = ((x + 1)/x)/((x ā 1)/x) = (x + 1)/x Ć š„/(š„ ā 1) = (š„ + 1)/(š„ ā 1 ) So, f(x) = (š„ + 1)/(š„ ā 1 ) ā“ f(x) = š¢/š£ So, fā(x) = (š¢/š£)^ā² = (u^ā² v ā v^ā² u)/v^2 Now, u = x + 1 uā = 1 + 0 = 1 v = x ā 1 vā = 1 ā 0 = 1 Now, fā(x) = (š¢/š£)^ā² = (š¢^ā² š£ āć š£ć^ā² š¢)/š£^2 = (1 (x ā 1) ā1 (x + 1) )/(x ā 1)^2 = (x ā 1 ā x ā 1)/(x ā 1)^2 = (ā 2)/(x ā 1)^2 Hence, fā (x) = (ā š)/(š± ā š)^š