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Formula sheet for Prelim 1 in Math 106
Differentiation formulas
(x
p
)
′
= px
p1
(e
x
)
′
= e
x
(ln x)
′
= 1/x
(cf)
′
= cf
′
(f+g)
′
= f
′
+g
′
(fg)
′
= f
′
g + f g
′
(1/g)
′
=  g
′
/ g
2
(f/g)
′
= (f
′
g  f g
′
) / g
2
(f(g))
′
= f
′
(g) g
′
Leibniz view of the chain rule:
df
df
dg
dx
dg
dx
=
⋅
Equation of the tangent line to the graph at x
0
:
00
0
()
'
(
)
yf
x
f
xx
x
=+
−
Algebra, Properties of e and ln:
(a+b)
2
= a
2
+ 2ab + b
2
1
lim
1
2.71828
n
n
e
n
→∞
⎛⎞
+=
=
⎜⎟
⎝⎠
Definition.
e
ln x
=
x
l
n
(
e
x
) = x
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This note was uploaded on 11/14/2007 for the course MATH 1106 taught by Professor Durrett during the Spring '07 term at Cornell University (Engineering School).
 Spring '07
 DURRETT
 Calculus, Chain Rule, The Chain Rule, Formulas

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