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Derivative?
f(x)= sinx
Answer
f'(x)= cosx
Derivative?
x
xf
1
)( =
Answer
2
1
)('
x
xf −=
What does this mean?
?lim
0
=
−+
→ h
ee xhx
h
Answer:
It is asking for the
derivative of ex
. The
notation is the limit
definition of the derivative
(difference quotient)
Derivative?
)(
)(
xg
xf
y =
Answer-Quotient Rule
( )
LowLow
HighDLowLowDHigh
y
xg
xgxfxfxg
y
−
=
−
=
'
)(
)(')()(')(
' 2
Derivative?
f(x)= ax
Answer
aaxf x
ln)(' =
Derivative?
f(x)= cotx
Answer
f'(x)= -csc2
x
Derivative?
f(x)= secx
Answer
f'(x)= secxtanx
Derivative?
f(x)= arctanx= tan-1
x
Answer
2
1
1
)('
x
xf
+
=
Derivative?
f(x)= cosx
Answer
f'(x)= -sinx
Derivative?
f(x)= ex
Answer
f'(x)= ex
Derivative?
f(x)= arccosx= cos-1
x
Answer
2
1
1
)('
x
xf
−
−=
Derivative?
f(x)= tanx
Answer
f'(x)= sec2
x
Derivative?
f(x)= arccscx= csc-1
x
Answer
1||
1
)('
2
−
−=
xx
xf
Derivative?
f(x)= lnx
Answer
x
xf
1
)(' =
Derivative?
f(x)= cscx
Answer
f'(x)= -cscxcotx
Derivative?
y=f(x)g(x)
Answer-Product Rule
y'= f'(x)g(x)+f(x)g'(x)
Derivative?
f(x)= arcsinx= sin-1
x
Answer
2
1
1
)('
x
xf
−
=
Derivative?
f(x)= arccotx= cot-1
x
Answer
2
1
1
)('
x
xf
+
−=
Derivative?
f(x)= arcsecx= sec-1
x
Answer
1||
1
)('
2
−
=
xx
xf
Derivative?
xxf alog)(' =
Answer
ax
xf
ln
1
)(' =
Derivative?
y= f(g(x))
Answer-Chain Rule
y'= f'(g(x))g'(x)
dy=?
Answer
dy=f’(x)dx
y=?
Answer
y=f(x+ x)-f(x)
Derivative of Inverse
Answer
)('
1
)(' 1
yf
xf −
=

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