对数函数求导公式:(Inx)' = 1/x(ln为自然对数);(logax)' =x^(-1) /lna(a>0且a不等于1)。<br>对数的运算性质<br>当a>0且a≠1时,M>0,N>0,那么:<br>(1)log(a)(MN)=log(a)(M)+log(a)(N);<br>(2)log(a)(M/N)=log(a)(M)-log(a)(N);<br>(3)log(a)(M^n)=nlog(a)(M) (n∈R)<br>(6)换底公式:log(A)M=log(b)M/log(b)A (b>0且b≠1)<br>设a=n^x则a^(log(b)n)=(n^x)^log(b)n=n^(x·log(b)n)=n^log(b)(n^x)=n^(log(b)a)<br>log(a)a^b=b 证明:设a^log(a)N=X,log(a)N=log(a)X,N=X<br>基本初等函数求导公式<br>对数与指数之间的关系<br>当a大于0,a不等于1时,a的X次方=N等价于log(a)N=x<br>log(a^k)(M^n)=(n/k)log(a)(M)(n属于R)<br>换底公式(很重要)<br>log(a)(N)=log(b)(N)/log(b)(a)=lnN/lna=lgN/lga<br>ln自然对数以e为底e为无限不循环小数(通常情况下只取e=2.71828)<br>lg常用对数以10为底