微分公式： 1. 2. 3. 4. 5. 6. 7. 8. 9.
dn
(x)=nxn−1 dx
dax
(e)=aeax dx
d1(lnx)=,dxx
x>0
d
sinax=acosx dx
d
cosax=−asinx dx
d
sinhx=coshx dx
d
coshx=sinhx dx
d
[cf(x)]=cf'(x) dx
ddd
f(x)±g(x)=f'(x)+g'(x) [f(x)±g(x)]=
dxdxdx
d
[f(x)⋅g(x)]=f'(x)g(x)+f(x)g'(x) dx
10. product rule：11. quotient rule：
d⎡f(x)⎤f'(x)g(x)−f(x)g'(x)
= ⎢⎥2
dx⎣g(x)⎦[g(x)]
dfdgd
f(g(x))=⋅=f'(g(x))g'(x) dxdgdx
12. the chain rule：
積分公式： 1.
⎧lnx+c,for n=−1⎪n+1=xdx ⎨x∫+≠−c,for n1⎪⎩n+1
nax
∫edx=
2. 3. 4. 5. 6. 7. 8. 9. 10.
1ax
e+c a
1
sinaxdx=−cosax+c ∫a
∫cosaxdx=
ax
1
sinax+c a
eax
∫esinbxdx=a2+b2[asinbx−bcosbx] eax
∫ecosbxdx=a2+b2[acosbx+bsinbx]
ax
∫[cf(x)]dx=c∫f(x)dx
∫[f(x)±g(x)]dx=∫f(x)dx±∫g(x)dx
d
[cf(x)]=cf'(x) dx
∫udv=u⋅v−∫vdu
