新高考數(shù)學(xué)一輪復(fù)習(xí) 講與練第9講 導(dǎo)數(shù)的概念及運(yùn)算（原卷版）

第9講導(dǎo)數(shù)的概念及運(yùn)算學(xué)校____________姓名____________班級(jí)____________一、知識(shí)梳理1.導(dǎo)數(shù)的概念(1)稱函數(shù)y＝f(x)在x＝x0處的瞬時(shí)變化率為函數(shù)y＝f(x)在x＝x0處的導(dǎo)數(shù)，記作f′(x0)，即f′(x0)＝.(2)在f(x)的定義域內(nèi)，f′(x)是一個(gè)函數(shù)，這個(gè)函數(shù)通常稱為函數(shù)y＝f(x)的導(dǎo)函數(shù)，記作f′(x)(或y′，yx′)，即f′(x)＝y(tǒng)′＝y(tǒng)x′＝，導(dǎo)函數(shù)也簡稱為導(dǎo)數(shù).2.導(dǎo)數(shù)的幾何意義f′(x0)是曲線y＝f(x)在點(diǎn)(x0，f(x0))處的切線的斜率，從而在點(diǎn)(x0，f(x0))處的切線方程為y－f(x0)＝f′(x0)·(x－x0).3.基本初等函數(shù)的導(dǎo)數(shù)公式(1)C′＝0；(2)(xα)′＝α·xα－1；(3)(ax)′＝ax·lna；(4)(logax)′＝eq\f(1,xlna)；(5)(sinx)′＝cosx；(6)(cosx)′＝－sinx；(7)(ex)′＝ex；(8)(lnx)′＝eq\f(1,x).4.導(dǎo)數(shù)的運(yùn)算法則如果f(x)，g(x)都可導(dǎo)，則有：(1)[f(x)±g(x)]′＝f′(x)±g′(x)；(2)[f(x)g(x)]′＝f′(x)g(x)＋f(x)g′(x)；(3)eq\b\lc\[\rc\](\a\vs4\al\co1(\f(f（x）,g（x）)))′＝eq\f(f′（x）g（x）－f（x）g′（x）,[g（x）]2)(g(x)≠0)；(4)[Cf(x)]′＝Cf′(x).5.復(fù)合函數(shù)的導(dǎo)數(shù)如果函數(shù)y＝f(u)與u＝g(x)的復(fù)合函數(shù)為y＝h(x)＝f(g(x))，則復(fù)合函數(shù)的導(dǎo)數(shù)h′(x)與f′(u)，g′(x)之間的關(guān)系為h′(x)＝[f(g(x))]′＝f′(u)·g′(x)＝f′(g(x))·g′(x)，即yx′＝y(tǒng)u′·ux′.考點(diǎn)和典型例題1、導(dǎo)數(shù)的概念及幾何意義【典例1-1】（2022·河北·模擬預(yù)測(cè)）曲線SKIPIF1<0在SKIPIF1<0處的切線斜率為（

）A．0 B．1 C．2 D．SKIPIF1<0【典例1-2】（2022·山東棗莊·三模）曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線與直線SKIPIF1<0垂直，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例1-3】（2022·湖北·宜城市第一中學(xué)高三階段練習(xí)）若過點(diǎn)SKIPIF1<0可以作曲線SKIPIF1<0的兩條切線，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0且SKIPIF1<0【典例1-4】（2022·廣西廣西·模擬預(yù)測(cè)（理））曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例1-5】（2022·河南洛陽·三模（理））若過點(diǎn)SKIPIF1<0可作出曲線SKIPIF1<0的三條切線，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02、導(dǎo)數(shù)的運(yùn)算【典例2-1】（2022·陜西·西安中學(xué)模擬預(yù)測(cè)（文））已知函數(shù)SKIPIF1<0的導(dǎo)函數(shù)為SKIPIF1<0，且滿足SKIPIF1<0，則SKIPIF1<0（

）A．1 B．SKIPIF1<0 C．-1 D．SKIPIF1<0【典例2-2】（2022·全國·河源市河源中學(xué)模擬預(yù)測(cè)）已知實(shí)數(shù)x滿足SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，那么SKIPIF1<0的值為(

)A．0 B．1 C．2 D．SKIPIF1<0【典例2-3】（2022·全國·高三專題練習(xí)）若函數(shù)SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0（

）A．1 B．2 C．3 D．4【典例2-4】（2022·江蘇鹽城·三模）已知SKIPIF1<0為SKIPIF1<0的導(dǎo)函數(shù)，且滿足SKIPIF1<0，對(duì)任意的SKIPIF1<0總有SKIPIF1<0，則不等式SKIPIF1<0的解集為__________．【典例2-5】（2022·全國·贛州市第三中學(xué)模擬預(yù)測(cè)（理））已知SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，那么SKIPIF1<0___________.3、導(dǎo)數(shù)運(yùn)算的綜合【典例3-1】（2020·陜西·咸陽市高新一中高三階段練習(xí)（理））已知SKIPIF1<0，且SKIPIF1<0，則實(shí)數(shù)a的值為(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例3-2】（2022·河南·方城第一高級(jí)中學(xué)模擬預(yù)測(cè)（理））已知直線l的斜率為2，l與曲線SKIPIF1<0：SKIPIF1<0和圓SKIPIF1<0：SKIPIF1<0均相切，則SKIPIF1<0（

）A．－4 B．－1 C．1 D．4【典例3-3】（2022·山西太原·二模（理））已知函數(shù)SKIPIF1<0圖象上存在兩條互相垂直的切線，且SKIPIF1<0，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例3-4】（2022·江西南昌·二模（理））已知函數(shù)fSKIPIF1<0SKIPIF1<0，若函數(shù)SKIPIF1<0的圖象上存在兩個(gè)點(diǎn)SKIPIF1<0，SKIPIF1<0，滿足SKIPIF1<0，則a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKI