Differentiation - Natural Logs and Exponentials Date Period - Kuta Software
Kuta Software - Infinite Calculus
Name___________________________________
Differentiation - Natural Logs and Exponentials
Date________________ Period____
Differentiate each function with respect to x. 1) y = ln x3
2) y = e2x3
3) y = ln ln 2x4
4) y = ln ln 3x3
5) y = cos ln 4x3
6) y = ee3x2
7) y = e(4x3 + 5)2
8) y = ln 4x2 (-x3 - 4)
( )4x4 5
9)
y = ln
- x3 - 3
e5x4 10) y = e4x2 + 3
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus
Name___________________________________
Differentiation - Natural Logs and Exponentials
Date________________ Period____
Differentiate each function with respect to x.
1) y = ln x3
dy dx
=
1 x3
3x2
3 =
x
2) y = e2x3 dy = e2x3 6x2 dx
3) y = ln ln 2x4
dy dx
1 =
ln 2x4
1
2 x4
8x3
4 = x ln 2x4
4) y = ln ln 3x3
dy dx
1 =
ln 3x3
1
3 x3
9x2
3 = x ln 3x3
5) y = cos ln 4x3
dy dx
= -sin ln 4x3
1
4x3
12x2
3sin ln 4x3 = -
x
6) y = ee3x2
dy = e e e3x2 3x2 6x dx
= 6xee3x2 + 3x2
7) y = e(4x3 + 5)2
dy = e(4x3 + 5)2 2(4x3 + 5) 12x2
dx
= 24x2e(4x3 + 5)2 (4x3 + 5)
8) y = ln 4x2 (-x3 - 4)
dy dx
= ln 4x2
-3 x2
+
(-x3
-
4)
1 4x2
8x
-3x3 ln 4x2 - 2x3 - 8 =
x
( )4x4 5
9)
y = ln
- x3 - 3
( ) dy = 5
dx
1 -4 x4
-16x3 -
1 x3 - 3
3x2
5(x3 - 12) = x(x3 - 3) (Rules of logarithms used)
e5x4 10) y = e4x2 + 3
( ) dy = e5x4 - (4x2 + 3) 20x3 - 8x
dx
( ) = 4xe5x4 - 4x2 - 3 5x2 - 2 (Rules of exponents used)
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Worksheet by Kuta Software LLC
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