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Last updated at April 16, 2024 by Teachoo

Misc 8 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): (ax + b)/(px2 + qx + r) Let f(x) = (šš„ + š)/(šš„2 + šš„ + š) Let u = ax + b & v = px2 +qx+ r ā“ f(x) = š¢/š£ So, fā(x) = (š¢/š£)^ā² fā(x) = (š¢^ā² š£ ā š£^ā² š¢)/š£^2 Finding uā & vā u = ax + b uā = a Ć 1 + 0 uā = a v = px2 + qx + r vā= p Ć 2x + q Ć 1 + 0 vā = 2px + q fā(x) = (š¢/š£)^ā² = (š¢^ā² š£ āć š£ć^ā² š¢)/š£^2 = (š (šš„2 + šš„ + š ) ā (2šš„ + š) (šš„ + š) )/(šš„2+ šš„ + š)2 = (ššš„2 + ššš„ + šš ā 2šš„ (šš„ + š) ā š (šš„ + š) )/(šš„2+ šš„ + š)2 = (ššš„2 ā 2ššš„2 + ššš„ ā ššš„ ā 2ššš„ ā šš + šš )/(šš„2+ šš„ + š)2 = (ā ššš„2 ā 2ššš„ ā šš + šš )/(šš„2+ šš„ + š)2 = (ā ššš„2 ā 2ššš„ + šš ā šš)/(šš„2+ šš„ + š)2 So, fā(x) = (ā šššš ā šššš + šš ā šš)/(ššš+ šš + š)š