A Derivatives You are expected to have the following facts memorized.
d 1. -xn
dx
= nxn-1
d
2. -d Vx
x
1
= 2yx r,;
d 1 3. -lnx = dx
x
d 4. dx logbx
1
1 lnb
=;
d
6. -ax= axlna
dx
d
d . 7 . dx smx = cosx,
.
dx cosx = -smx
8. dx tanx =sec x,
d 2 dx cot x = - csc x
d 9. dx secx = secxtanx,
d dx cscx = - cscx cot x
d
d . x
10. -d Slll
2
1
-1
~' 2
X=
v 1- x
d -1 -1 -d cos x= ~2 x v 1- x
d -1 1 11. -d tan x = - -2 , x 1 +x
d -1 -1 -cot x = - -2 dx 1+x
d -1 12. dxsec x=
-csc- 1 x = - - - dx lx1Jx 2 - 1
13.
d~ sinh x =
1 ~' lxlvx 2 - 1
cosh x,
d
d~ cosh x =
-l
sinh x