Miscellaneous

Chapter 12 Class 11 Limits and Derivatives
Serial order wise

### Transcript

Misc 9 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): (px2 + qx + r)/(ax + b) Let f(x) = (šš„2 + šš„ + š)/(šš„ + š) Let u = px2 + qx + r & v = ax + b ā“ f(x) = š¢/š£ So, fā(x) = (š¢/š£)^ā² fā(x) = (š¢^ā² š£ ā š£^ā² š¢)/š£^2 Finding uā & vā u = px2 + qx + r uā = p Ć 2x + q Ć 1 + 0 uā = 2px + q v = ax + 3 vā= a Ć 1 + 0 vā = a fā(x) = (š¢/š£)^ā² = (š¢^ā² š£ āć š£ć^ā² š¢)/š£^2 = ((2šš„ + š) (šš„ + š) ā a (px2 + šš„ + š) )/(ax + b)2 = (2ššš„2 + 2ššš„ + ššš„ + šš ā ššš„2 ā ššš„ ā šš)/(ax + b)2 = (ššš„2 + 2ššš„ + šš ā šš )/(ax + b)2 ā“ fā(x) = (šššš + šššš + šš ā šš)/(šš + š)š