Lim     sin(x)

x->0      x

 d  [cu]

dx

 d  [u+-v]

dx

 d  [uv]

dx

 d  [u/v]

dx

vu'-uv'

v²

 d  [c]

dx

 d  [uⁿ]

dx

 d  [x]

dx

 d  [ln u]

dx

u'

u

 d  [e^u]

dx

 d  [f(g(x))]

dx

 d  [sin u]

dx

 d  [cos u]

dx

 d  [tan u]

dx

 d  [csc u]

dx

 d  [sec u]

dx

 d  [cot u]

dx

 d  [arcsin u]

dx

u'

sqrt(1-u²)

 d  [arccos u]

dx

-u'

sqrt(1-u²)

 d  [arctan u]

dx

u'

1+u²

 d  [arccsc u]

dx

-u'

|u|sqrt(u²-1)

 d  [arcsec u]

dx

u'

|u|sqrt(u²-1)

 d  [arccot u]

dx

-u'

1+u²

Given function f'(x). g(x)=f^-1(x)

What is g'(x)

1

f'(g(x))

If f is continuous on [a,b] and differentiable on (a,b), then there exists a number c in (a,b) such that:

f'(c) = f(b)-f(a)

         b-a

x^n+1  + C

n+1

a^x + C

ln a

∫1 dx

x

∫1 dx

sqrt(a²-x²)

arcsin x  + C

  a

∫1 dx

a²+x²

1 arctan x  + C

a          a

∫1  dx

x*sqrt(x²-a²)

1 arcsec x  + C

a          a

_b

∫ f(x) dx = F(b)-F(a)

^a

_x

d  ∫ f(t) dt = f(x)x'

dx   ^a  

1   _b

---- ∫f(x) dx

b-a ^a

log x

log a

(1-cos 2θ)

2

(1+cos 2θ)

2

πr²h

3

4πr³

3