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The Natural Logarithmic Function- HW Problems
Find the derivative of the following functions.
1. 𝑦 = 𝑥𝑙𝑛(𝑥)
2. 𝑦 = cos[ln(𝑥 )]
3. 𝑓(𝑥 ) = [ln(𝑥 )]2
4. 𝑔(𝑥 ) = ln(𝑥 2 )
5. 𝑦 = ln(𝑥 2 √1 + 𝑥 2 )
1−𝑥2
6. 𝑦 = ln (√ )
1+𝑥2
7. 𝑦 = ln[𝑐𝑜𝑠(𝑡)]
8. 𝑓(𝑥 ) = ln[cos2 (𝑡)]
9. 𝑓(𝑥 ) = [ln(𝑡𝑎𝑛(𝑥 ))]3
10. 𝑔(𝜃 ) = ln[𝑠𝑒𝑐 (𝜃 ) + 𝑡𝑎𝑛(𝜃 )]
Evaluate the following integrals.
𝑥 𝑒 𝑥 2 −1
11. ∫ 𝑥 2 +1 𝑑𝑥 14. ∫1 𝑥 𝑑𝑥
𝑑𝑥 𝑒 (ln(𝑥))4
12. ∫ 4+5𝑥 15. ∫1 𝑥 𝑑𝑥
𝜋
sin(𝑥) 𝑥+1
13. ∫0 1+cos(𝑥) 𝑑𝑥
2 16. ∫ 𝑥 2 +2𝑥−6 𝑑𝑥.
The Natural Logarithmic Function- HW Problems
Find the derivative of the following functions.
1. 𝑦 = 𝑥𝑙𝑛(𝑥)
2. 𝑦 = cos[ln(𝑥 )]
3. 𝑓(𝑥 ) = [ln(𝑥 )]2
4. 𝑔(𝑥 ) = ln(𝑥 2 )
5. 𝑦 = ln(𝑥 2 √1 + 𝑥 2 )
1−𝑥2
6. 𝑦 = ln (√ )
1+𝑥2
7. 𝑦 = ln[𝑐𝑜𝑠(𝑡)]
8. 𝑓(𝑥 ) = ln[cos2 (𝑡)]
9. 𝑓(𝑥 ) = [ln(𝑡𝑎𝑛(𝑥 ))]3
10. 𝑔(𝜃 ) = ln[𝑠𝑒𝑐 (𝜃 ) + 𝑡𝑎𝑛(𝜃 )]
Evaluate the following integrals.
𝑥 𝑒 𝑥 2 −1
11. ∫ 𝑥 2 +1 𝑑𝑥 14. ∫1 𝑥 𝑑𝑥
𝑑𝑥 𝑒 (ln(𝑥))4
12. ∫ 4+5𝑥 15. ∫1 𝑥 𝑑𝑥
𝜋
sin(𝑥) 𝑥+1
13. ∫0 1+cos(𝑥) 𝑑𝑥
2 16. ∫ 𝑥 2 +2𝑥−6 𝑑𝑥.
