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导数表和基本积分表

\[\begin{aligned} 1.&f(x)=C,f'(x)=0\\ 2.&f(x)=x^n,f'(x)=nx^{n-1}\\ 3.&f(x)=a^x,f'(x)=ln\ a\times a^x\\ 4.&f(x)=e^x,f'(x)=e^x\\ 5.&f(x)=log_ax,f'(x)=\frac{1}{x\times ln\ a}\\ &(f(x)=ln\ x,f'(x)=\frac{1}{x})\\ 6.&f(x)=sin\ x,f'(x)=cos\ x\\ 7.&f(x)=cos\ x,f'(x)=-sin\ x\\ 8.&f(x)=tan\ x,f'(x)=\frac{1}{cos^2x}\\ 9.&f(x)=cot\ x,f'(x)=-\frac{1}{sin^2x}\\ 10.&f(x)=g[h(x)],f'(x)=g'[h(x)]h'(x)\\ 11.&f(x)=g(x)h(x),f'(x)=g'(x)h(x)+g(x)h'(x)\\ 12.&f(x)=\frac{g(x)}{h(x)},f'(x)=\frac{[g'(x)h(x)-g(x)h'(x)]}{h^2(x)}\\ \end{aligned}\]
\[\begin{aligned} 1.&\int k\ dx=kx+C\\ 2.&\int k^\mu dx=\frac{x^{\mu +1}}{\mu +1}+C (\mu \not= -1)\\ 3.&\int\frac{dx}{x}=ln|x|+C\\ 4.&\int\frac{dx}{1+x^2}=arctan\ x+C\\ 5.&\int\frac{dx}{sqrt{1+x^2}}=arcsin\ x+C\\ 6.&\int cos\ x\ dx=sin\ x+C\\ 7.&\int sin\ x\ dx=-cos\ x+C\\ 8.&\int \frac{dx}{cos^2x}=\int sec^2xdx=tan\ x+C\\ 9.&\int \frac{dx}{sin^2x}=\int csc^2xdx=-cot\ x+C\\ 10.&\int sec\ x\ tan\ x\ dx=sec\ x+C\\ 11.&\int csc\ x\ cot\ x\ dx=-csc\ x+C\\ 12.&\int e^x\ dx=e^x+C\\ 13.&\int a^x\ dx=\frac{a^x}{ln\ a}+C\\ \end{aligned}\]



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