

Last updated at Dec. 8, 2016 by Teachoo
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Misc 5 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): šš„ + šļ·®šš„ + šļ·Æ Let f(x) = šš„ + šļ·®šš„ + šļ·Æ Let u = ax + b & v = cx + d ā“ f(x) = š¢ļ·®š£ļ·Æ So, fā(x) = š¢ļ·®š£ļ·Æļ·Æļ·®ā²ļ·Æ fā(x) = š¢ļ·®ā²ļ·Æš£ ā š£ļ·®ā²ļ·Æš¢ļ·® š£ļ·®2ļ·Æļ·Æ Finding u & v u = ax + b uā = a + 0 = a v = cx + d vā = c + 0 = c fā(x) = š¢ļ·®š£ļ·Æļ·Æļ·®ā²ļ·Æ = š¢ļ·®ā²ļ·Æš£ ā š£ļ·®ā²ļ·Æš¢ļ·® š£ļ·®2ļ·Æļ·Æ = š šš„ + šļ·Æ ā š (šš„ + š)ļ·® šx + dļ·Æ2ļ·Æ = acx + ad ā ššš„ ā ššļ·® cx + šļ·Æ2ļ·Æ = acx + ad ā ššš„ ā ššļ·® cx + šļ·Æ2ļ·Æ = ad ā cbļ·® cx + šļ·Æ2ļ·Æ Hence, fā (x) = šš ā ššļ·® šš± + š ļ·Æšļ·Æ
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