03 - Chain Rule with Logs Exponentials - Kuta Software

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Kuta Software - Infinite Calculus

Name___________________________________

Differentiation - Logs and Exponentials

Date________________ Period____

Differentiate each function with respect to x. 1) y = 4

4x4

2) y = 4

3) y = log 3 3 x 2

5) y = log 3 (3 x 5 + 5)

7) y = (4 + 2) x3

9) y = 3

−5 x 3

4) y = log 2 4 x 2

5

6) y = log 5 (−5 x 3 − 2)

3

cos 3 x 4

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8) y = 3

3

( x 4 + 1) 3

10) y = log 5 tan 4 x 4

Worksheet by Kuta Software LLC

Kuta Software - Infinite Calculus

Name___________________________________

Differentiation - Logs and Exponentials

Date________________ Period____

Differentiate each function with respect to x. 1) y = 4

4x4

2) y = 4

dy −5 x 3 =4 ln 4 ⋅ −15 x 2 dx 15 x 2 ln 4 =− 5x3 4

dy 4x4 = 4 ln 4 ⋅ 16 x 3 dx 4 x4 + 2 = x3 ⋅ 4 ln 4

3) y = log 3 3 x 2

4) y = log 2 4 x 2

1 dy = 2 ⋅ 6x dx 3 x ln 3 2 = x ln 3

5) y = log 3 (3 x 5 + 5)

1 dy = 2 ⋅ 8x dx 4 x ln 2 2 = x ln 2

5

6) y = log 5 (−5 x 3 − 2)

1 dy = ⋅ 5(3 x 5 + 5) 4 ⋅ 15 x 4 5 dx (3 x 5 + 5) ln 3 75 x 4 = ln 3 ⋅ (3 x 5 + 5)

7) y = (4 + 2) x3

8) y = 3

2

= 9 x 2 (4 x + 2) ⋅ 4 x ln 4 3

3

( x 4 + 1) 3

dy ( x 4 + 1) 3 2 =3 ln 3 ⋅ 3( x 4 + 1) ⋅ 4 x 3 dx (

= 4x3 ⋅ 3 x

4

3

+ 1) + 1

⋅ ( x 4 + 1) 2 ln 3

10) y = log 5 tan 4 x 4

cos 3 x 4

dy cos 3 x 4 =3 ln 3 ⋅ −1sin 3 x 4 ⋅ 12 x 3 dx = −4 x 3 ⋅ 3

3

1 dy = ⋅ 3(−5 x 3 − 2) 2 ⋅ −15 x 2 3 dx (−5 x 3 − 2) ln 5 45 x 2 =− ln 5 ⋅ (−5 x 3 − 2)

3

3 3 2 dy = 3(4 x + 2) ⋅ 4 x ln 4 ⋅ 3 x 2 dx

9) y = 3

−5 x 3

cos 3 x 4 + 1

sin 3 x 4 ⋅ ln 3

1 dy = ⋅ sec 2 4 x 4 ⋅ 16 x 3 4 dx tan 4 x ⋅ ln 5 16 x 3 ⋅ sec 2 4 x 4 = tan 4 x 4 ⋅ ln 5

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Worksheet by Kuta Software LLC