基礎(chǔ)復(fù)合函數(shù)二階導(dǎo)數(shù)練習(xí)題及答案步驟A7

基礎(chǔ)復(fù)合函數(shù)二階導(dǎo)數(shù)練習(xí)題及答案步驟?1：求y=(9x+47)4二階導(dǎo)數(shù)。?2：求y=eq\r(82-x2)的二階導(dǎo)數(shù)。?3：求y=e4x二階導(dǎo)數(shù)y"的計(jì)算過(guò)程。?4：計(jì)算y=sin(18x+34)的二階導(dǎo)數(shù)。?5：求y=eeq\s\up8(10x2cos3x+39x)二階導(dǎo)數(shù)。?6：求y=ln(11x-eq\r(4x2-52))的二階導(dǎo)數(shù)。參考答案一、基礎(chǔ)復(fù)合函數(shù)二階導(dǎo)數(shù)?1：求y=(9x+47)4二階導(dǎo)數(shù)。解：y=(9x+47)4，y'=4(9x+47)3*9,=36(9x+47)3，y"=36*3(9x+47)2*9,=972(9x+47)2。?2：求y=eq\r(82-x2)的二階導(dǎo)數(shù)。解：y=eq\r(82-x2)，y'=eq\f(1,2)*eq\f(1,eq\r(82-x2))*(82-x2)'，=eq\f(1,2)*eq\f(1,eq\r(82-x2))*(-2x)=-eq\f(x,eq\r(82-x2))，y"=-eq\f(eq\r(82-x2)-x*eq\f(1,2)*eq\f(-2x,eq\r(82-x2)),82-x2)，=-eq\f(82,eq\r((82-x2))3)。?3：求y=e4x二階導(dǎo)數(shù)y"的計(jì)算過(guò)程。解：y=e4x，y'=e4x*4,y"=e4x*4*4=42*e4x。?4：計(jì)算y=sin(18x+34)的二階導(dǎo)數(shù)。解：y=sin(18x+34)，y'=cos(18x+34)*18,y"=-sin(18x+34)*18*18,=-182*sin(18x+34)。?5：求y=eeq\s\up8(10x2cos3x+39x)二階導(dǎo)數(shù)。解：y=eeq\s\up8(10x2cos3x+39x)，y'=eeq\s\up8(10x2cos3x+39x)*[10(2xcos3x-x2sin3x*3)+39],y'=y[10(2xcos3x-x2sin3x*3)+39],y"=y'[10(2xcos3x-x2sin3x*3)+39]+10(2cos3x-2xsin3x*3-2xsin3x*3-x2cos3x*32)y。?6：求y=ln(11x-eq\r(4x2-52))的二階導(dǎo)數(shù)解：y=ln(11x-eq\r(4x2-52)),y'=eq\f(11-\f(4x,eq\r(4x2-52)),11x-eq\r(4x2-52)),=eq\f(11eq\r(4x2-52)-4x,eq\r(4x2-52)(11x-eq\r(4x2-52)))=eq\f(A,B),y"=EQ\f(A'B-AB',B2),其中：A'=eq\f(11*4,eq\r(4x2-52))-4,B'=eq\f(4,eq\r(4x2-52))(11x-eq\r(4x2-52))+eq\r(4x2-52)*(11-eq\f(4,