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The Chain Rule- HW Problems
Find the derivatives.
1. 𝑦 = (𝑥 2 + 1)30
2. 𝑓(𝑡) = (𝑡 3 − 2𝑡)5
5
𝑥2
3. 𝑔(𝑥 ) = (1+𝑥3 )
4. 𝑦 = (3𝑥 + 2)4 (𝑥 2 − 𝑥 )3
5. 𝑓(𝑥 ) = cos (𝑥 2 + 2𝑥 − 4)
6. 𝑔(𝜃 ) = sin4 (3𝜃)
7. 𝑦 = (csc(𝑡) + 𝑡 2 )8
8. 𝑓(𝑥 ) = 𝑥 2 tan(𝑥 2 )
sec(𝑥) 3
9. 𝑔(𝑥 ) = ( )
1+sec(𝑥)
10. 𝑦 = sin[cos(𝑥 4 )]
11. 𝑓 (𝑥 ) = cos3 (𝑥 8 )
1+𝜃
12. 𝑦 = tan ( )
1−𝜃
13. Find the second derivative of 𝑦 = sin(𝑥 2 ).
The Chain Rule- HW Problems
Find the derivatives.
1. 𝑦 = (𝑥 2 + 1)30
2. 𝑓(𝑡) = (𝑡 3 − 2𝑡)5
5
𝑥2
3. 𝑔(𝑥 ) = (1+𝑥3 )
4. 𝑦 = (3𝑥 + 2)4 (𝑥 2 − 𝑥 )3
5. 𝑓(𝑥 ) = cos (𝑥 2 + 2𝑥 − 4)
6. 𝑔(𝜃 ) = sin4 (3𝜃)
7. 𝑦 = (csc(𝑡) + 𝑡 2 )8
8. 𝑓(𝑥 ) = 𝑥 2 tan(𝑥 2 )
sec(𝑥) 3
9. 𝑔(𝑥 ) = ( )
1+sec(𝑥)
10. 𝑦 = sin[cos(𝑥 4 )]
11. 𝑓 (𝑥 ) = cos3 (𝑥 8 )
1+𝜃
12. 𝑦 = tan ( )
1−𝜃
13. Find the second derivative of 𝑦 = sin(𝑥 2 ).
