basic derivatives

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...

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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