Calculus1
Notes
Name_PowerRule
DerivativesSlopeofaTangent
Theexpressionfoundwhendeterminingtheexpressionfortheslopeofatangent( m t an )forafunctioniscalledthederivative
ofthefunction.Thederivativeisusedtofindtheinstantaneousrateofchangeforanyvalueoftheind
Day0Notes(Thursday21711)
f (x
) =2 x
f (x ) =
1
x +1
at
x =- 5
-3
mtan=
mtan=
g (x
) =4 x
2
+7
f ( x ) =x
3
at
mtan=
x =3
mtan=
Day0Hmwk(Thursday21711)
f (x
)
Day1Homework(Friday2/18/11)
= 7 x +11
1.f ( x ) =x
2
+1
at
x =2
mtan=
mtan=
g (x
2.f
Calculus1
Name
WorksheetProductandQuotientRules
Date
Findthederivativesofthegivenfunctionsusingtheproductandquotientrules.
1) y =( 3 x
2
(
+6 ) 2 x - 1
4
1
y = ( 6 x ) x - 3 x
2
+
4
(
3) y =( x
3
+7 x
(
2
+14 x
(
-2
y = 3x
y = -x
5) y =( 3 x
(
y = 3x
Calculus1
LessonProblems
SlopeofaTangentLineLimitDefinition
f (x 2 ) - f (x1)
f ( x +h ) - f ( x )
msec =
m t an =lim
wh e r e h =( x +h ) - x
h 0
x2 - x1
h
Usethelimitdefinitiontofind(a)theequationfortheslopeofanytangentlineforeachcurve(b)theslopeofthe
t
vaTive of The following funcTions
1x5cosx 2) y=cosxTanX.
:X 4)y : (3x3 + 2x)coTx
for' y : sin xcosx 6) Find f"(x) if f(x) = cosxTanx
value of x when The slope of The TangenT is equal To 2 for y 2 §x2 cos
for y : 3X cos X
) for' f(x) = (4X2 3x)sinx
equaTio