Page 12 - Math SL HB Sem 2

b) Defilative of e constant

If y: *"o rt =0,cisaconstant
"
c) Derivative of a coustant times a function

If y: c u(x) then Y' : " u'1,,

d) Derivative of ciicular trigonometric functions

Ifv = sin x theny' =cosx
tf v: cos x then Y' = -sln ;
Ify = tan x then Y' = t".' *

f) Derrvatives of elponential functions

If Y= e' 15sn Yr = qx
g) Derivatives of logarithmic functions
--rl
IfY=1n* $ea, =;

h) Derivative of a sum or dilference

:f(x) + g'(x)
li y = f(x) + g(x1 then Yt

i) Dciivative of a product of futrctions
i;-:j;)xc@ then vr=f(4's6) + f(x)xs'6)

j) Derivative of a quotient of functions
f{-r) t x
If v= i++ meny = /G) x s@ -f(x) s'G)
'
c(r)
[e(,X

k) Derivative of Composite functious
All functions that can be made up by composing a fimction of a function are called
comoosite functions.
For example iffk) : xa and g(x) = xz + 3x then

fG6):"fd+jx1 :(l+3x)4

Now considery = pc+ 1)3 which is really y = u3 where u-2x+ I
Exoandinewehavev: (2x + I)r
' : (2x)t + 3S2x)21 + 3Qx)12 + ti expansiorf
:81 + l2l + 6x+ I frbinomial

..0 =z4rr+ 24r+ 6
&
: 614a2 + 4x + l)

= 6Qx _ 1)2
:Jey+l)2x2

= 3u2 x \whichis ogoin!!-
& clu &