Derivatives Of Exponential Functions Worksheet - Calculus Maximus, Ch. 2.9
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4Calculus Maximus
Notes: 2.9 Exp Functions
§2.9—Derivatives of Exponential Functions
Example 1:
( )
( )
′
=
x
Sketch the graph of
f x
e
, then, on the same set of axes, sketch a possible graph of
f x
. What do
( )
′
you notice? Confirm by sketching
f x
using your calculator’s NDERIV capability.
x
Derivative of
e
d
d
⎡ ⎤ =
⎡ ⎤
′
x
x
u
=
u
⋅
. If u is a differentiable function of x, then
(Chain Rule)
e
e
e
e u
⎣ ⎦
⎣ ⎦
dx
dx
Example 2:
( )
2
dy
+
x x
=
Find
if
y e
dx
Example 3:
( )
( )
′
f x =
x
Using your calculator, graph
2
and
using NDERIV. What do you notice? Do the same for
f x
( )
( )
x
′
g x =
5
and
g x
.
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