basic derivatives and integrals

d/dx(c) =

0

d/dx(mx) =

m

d/dx2=

2x

d/dx3

3(x2)

d/dx4=

4(x3)

d/dx(1/x)=

-1/x2

d/dx√x=

1/2√x

d/dx(sin x)=

cos x

d/dx (cos x)=

-sin x

d/dx (e(x))=

(e(to the power of x))

d/dx(a(to the power of x)=

a (to the power of x) (ln) a

d/dx (ln) |x|=

1/x

d/dx log(a) |x|

1/x (ln) a

∫0 dx =

C

∫cos x dx =

sin x + C

∫m dx =

mx + C

∫sin x dx =

-cos x + C

∫x dx =

½x2 + C

∫e(to the power of)x dx=

ex + C

∫ax dx=

ax/ln a + C

∫1/x dx =

ln |x| + C

∫1/x2 dx =

-1/x + C

∫1/√x dx =

2√x + C

∫ ln x dx =

x ln x - x + C