高等数学求导题50道 100道求导数计算题

求导公式c'=0(c为常数)(x^a)'=ax^(a-1),a为常数且a≠0(a^x)'=a^xlna(e^x)'=e^x(logax)'=1/(xlna),a>0且 a≠1(lnx)'=1/x(sinx)'=cosx(cosx)'=-sinx(tanx)'=(secx)^2(secx)'=secxtanx(cotx)'.

你好!1、y'=1/[3ln(ln3x)] * [ln(ln3x)] '= 1/[3ln(ln3x)] * 1/ln3x *(ln3x)'=1/[3ln(ln3x)] * 1/ln3x * 1/3x *3= 1/[3xln3xln(ln3x)] 是答案错了.2、f(0)=0,x→0时,sin2x→0∴极限是0/0型,由罗比达法则:lim f(x) / sin2x=lim f'(x) / (2cos2x)= f'(0) / 2cos0= 2/2 = 1

18.D y'=f'(lnx)*(1/x) y''=[f''(lnx)*(1/x)]*(1/x)+f'(lnx)*(-1/x^2) =(1/x^2)*[f''(lnx)-f'(lnx)] 20.C y'=x*1/x+1*lnx=1+lnx y''=1/x …… y(10)=(-1)(-2)……(-8)1/x^9=8!/x^9

两个函数在(1,-1)处的切线斜率相等 函数 2y = -1 + xy³ 求导 2y' = y³ + 3xy²y' 代入(1,-1)得到 2y' = 1 + 3y' 所以斜率为y' = -1 函数 y = x²+ax+b 求导得 y' = 2x + a = 2 + a 也等于-1 所以a = -3 且函数y = x²+ax+b 过(1,-1) ,所以 -1 = 1 + a + b 所以 b = -a -2 = 3 -2 =1 该点的斜率是-1 而且该点是(1,-1)所以切线方程是 (y+1) = -(x-1) 即 y = -x 法线斜率是1 所以切线方程是(y+1) = (x-1) 即y=x-2

y=(x³-x²)^(1/3)【解1】y'=(1/3)(x³-x²)^(-2/3)*(3x²-2x)=(x²-2x/3)(x³-x²)^(-2/3)【解2】lny=(1/3)ln(x³-x²)y'/y=(1/3)(3x²-2x)/(x³-x²)y'=y(x²-2x/3)/(x³-x²)=(x²-2x/3)(x³-x²)^(-2/3)取对数后求导数,对幂指函数,可简化计算.

y=tan(x+y)隐函数求导,两边分别求导.y'={[sec(x+y)]^2}(1+y')y'={[sec(x+y)]^2}/{1-[sec(x+y)]^2}y''=【2[sec(x+y)][sec(x+y)][tan(x+y)](1+y'){1-[sec(x+y)]^2}+{[sec(x+y)]^2*2[sec(x.

对数求导法 lny=tanx·lncosx 两边同时对x求导得到:1/y·y'=sec²x·lncosx+tanx·1/cosx·(-sinx)1/y·y'=sec²x·lncosx-tan²x ∴y'=y(sec²x·lncosx-tan²x)

y=x²ln(x+1)y'=2xln(x+1)+x²/(x+1)=2xln(x+1)+(x+1)+1/(x+1)-2y''=2ln(x+1)+2x/(x+1)+1-1/(x+1)^2=2ln(x+1)-2/(x+1)-1/(x+1)^2+3y'''=2/(x+1)+2/(x+1)^2+2(x+1)^3……y(n)=2(n-2)!(-1)^(n+1)[1/(x+1)^(n-2)+1/(x+1)^(n-1)+1/(x+1)^n-1(n≥3)y(50)=-2*48![1/(x+1)^48+1/(x+1)^49+1/(x+1)^50]

对x求导0.5*1/(x²+y²)*(x²+y²)'=1/[1+(y/x)²]*(y/x)'0.5/(x²+y²)*(2x+2y*y')=x²/[x²+y]*(y'*x-y*x')/x²x+y*y'=y'*x-yy'=(x+y)/(x-y)

解:1.(1)dy/dx=(dy/dt)/(dx/dt)=2t/2=t=x/2(2)dy/dx=(dy/dt)/(dx/dt)=e^t/(e^-t-te^-t)=y/(1/y-x)=y^2/(1-xy)2.y=x^x =e^(xlnx)lny=xlnxy'/y=lnx+1y'=y(lnx+1)=x^x(lnx+1)