一、基本函数求导公式
(egin {align} c' &= 0 \ x^n {'} &= nx^{n-1} \ a^x {'} &= a^xln a \ e^x {'} &= e^x \ log_ax' &= frac {1} {x ln a} \ ln x ' &= frac {1} {x} \ sin x' &= cos x \ cos x' &= -sin x end {align})
二、求导运算法则
(egin {align} (f(x) pm g(x))' &= f'(x) pm g'(x) \ (f(x)g(x))' &= f'(x)g(x) + f(x)g'(x) \ left(frac{f(x)}{g(x)} ight)' &= frac {f'(x)g(x) - f(x)g'(x)} {g(x)^2} \ (f(g(x)))' &= f'(g(x))g'(x) end {align})
三、常用积分公式
(egin {align} int x^nmathrm dx &= frac {1} {n+1}x^{n+1} + C (n e -1)\ int frac 1 x mathrm dx &= ln |x| + C end {align})
四、洛必达法则
若 (g(a)=0,h(a)=0)，那么(limlimits_{x→a}frac{g(x)}{h(x)}=limlimits_{x→a}frac{g'(x)}{h'(x)})