高中數(shù)學第二章 4_2 導數(shù)的乘法與除法法則 課件

第二章 變化率與導數(shù)4.2 導數(shù)的乘法與除法法則求函數(shù)的導數(shù)的步驟是怎樣的?(1)()();yf xxf x 求函數(shù)的增量(2):()();yf xxf xxx求函數(shù)的增量與自變量的增量的比值0(3)()lim.xyyfxx 求極限，得導函數(shù)導數(shù)公式表(其中三角函數(shù)的自變量單位是弧度).()()()(),()()()(xgxfxgxfxgxfxgxf兩個函數(shù)和(差)的導數(shù)等于這兩個函數(shù)導數(shù)的和(差),即:導數(shù)的加法和減法法則是什么?問題提出?),()()(2如何來求它的導數(shù)呢如果有函數(shù)xfxxgxfy分析推導),()()(,:0200200 xfxxxfxxyxx量可以得到函數(shù)值的改變的一個改變量首先給定自變量按照求函數(shù)導數(shù)的步驟),()()()()()()()()()()()()(020200020020200020020020 xfxxxxxxfxxfxxxxfxxxxfxxfxxxxfxxxfxxxy寫成相應(yīng)的平均變化率可以).()()()(,).(2)()()()(,2)(lim),()()(lim,)(lim,02220002002020200000020200 xfxxfxxfxxfxxfxxxfxxgxfxxxxxxfxxfxxfxxxxxxx的導數(shù)為因此處的導數(shù)值為在知由于令:),()()()(,我們有和是的導數(shù)分別和若兩個函數(shù)一般地xgxfxgxf.)()()()()()()(),()()()()()(2xgxgxfxgxfxgxfxgxfxgxfxgxf).()(:,)(,xf kxkfkxg有時當特別地.)()()()(),()()()(xgxfxgxfxgxfxgxf例題講解2.:(1);(2)sin1;(3)ln.xyx eyxxyxx求下面函例數(shù)的導數(shù).)2(2)(:,)(,2)(,)()()1(:22222xxxxxxxexxexxeexexgxxfexgxxfexy可得法則根據(jù)兩函數(shù)之積的求導由導數(shù)公式表分別得出之積與是函數(shù)函數(shù)解.cos2sin)sin(:,cos)(,21)(,sin)()(sin)2(xxxxxxxxgxxfxxgxxfxxy可得法則根據(jù)兩函數(shù)之積的求導由導數(shù)公式表分別得出之積與是函數(shù)函數(shù).1ln1ln1)ln(:,1)(,1)(,ln)()(ln)3(xxxxxxxxgxfxxgxxfxxy可得法則根據(jù)兩函數(shù)之積的求導由導數(shù)公式表分別得出之積與是函數(shù)函數(shù)2.:sin(1),(2)2.lnxxyyxx求下列函數(shù)的導數(shù)例.sincos1sincossin:,1)(,cos)(:,)(sin)(sin)1(:22xxxxxxxxxxxgxxfxxgxxfxxy由求導的除法法則得出根據(jù)導數(shù)公式表分別得之商和函數(shù)是函數(shù)函數(shù)解例題講解.ln)1ln2()(ln1ln2ln:,1)(,2)(:,ln)()(ln)2(222222xxxxxxxxxxxxgxxfxxgxxfxxy由求導的除法法則得出根據(jù)導數(shù)公式表分別得之商和函數(shù)是函數(shù)函數(shù)22.:cos(13)(lnsin);(2).xxyxxxyx求下列函數(shù)的導數(shù)例,cos1)(,2)(:.sinln)()()sin(ln)1(:22xxxgxxfxxxgxxfxxxy導法則可得的求由導數(shù)公式表及和函數(shù)的積與是函數(shù)函數(shù)解.cossin2ln2cos1)sin(ln2)sin(ln:222xxxxxxxxxxxxxxxx由求導的乘法法則可得例題講解,2)(,1sin)(:.)(cos)(cos)2(22xxgxxfxxgxxxfxxxy導法則可得的求由導數(shù)公式表及差函數(shù)的商與是函數(shù)函數(shù).cos2sin2cos2sin1)(2)(cos1sincos:332222xxxxxxxxxxxxxxxxxxx用求導的除法法則可得練習.)0,1(ln2)(的切線方程過點求曲線xxxfx.2ln2ln212ln2ln21ln2ln2)(:.ln2)(:xxxxxxxxfxxxfxxxxxxx的四則運算法則可得根據(jù)導數(shù)公式表和導數(shù)的導函數(shù)首先求出函數(shù)解).1(3)0,1(ln2)(.3121ln2ln21)1(),(111xyxxxffxfxx的切線方程為過點曲線得所求切線斜率代入將導數(shù)的乘法與除法法則是什么?.)()()()()()()(),()()()()()(2xgxgxfxgxfxgxfxgxfxgxfxgxf