Differentiation - Natural Logs and Exponentials Date Period

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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