Calculus derivative

Question 1

1. 𝑑/𝑑𝑥 [𝑐𝑓(𝑥)] =

Answer 1

𝑐𝑓′(𝑥)

Question 2

2. 𝑑/𝑑𝑥 [𝑓(𝑥) ± 𝑔(𝑥)] =

Answer 2

𝑐𝑓′(𝑥)

Question 3

3. Power Rule:𝑑/𝑑𝑥 [𝑥𝑛] = 𝑛𝑥𝑛−1

Question 4

4. Product Rule:𝑑/𝑑𝑥 [𝑓(𝑥)𝑔(𝑥)] = 𝑓(𝑥)𝑔′(𝑥) + 𝑔(𝑥)𝑓′(𝑥)

Question 5

5. Quotient Rule:𝑑/𝑑𝑥 [𝑓(𝑥)/𝑔(𝑥)] =𝑔(𝑥)𝑓′(𝑥) − 𝑓(𝑥)𝑔′(𝑥)/[𝑔(𝑥)]2

Question 6

6. Chain Rule:𝑑/𝑑𝑥 [𝑓(𝑔(𝑥))] = 𝑓′(𝑔(𝑥)) ∙ 𝑔′(𝑥)

Question 7

7. Inverse Rule:𝑑/𝑑𝑥 [𝑔(𝑥)] =1/𝑓′(𝑔(𝑥))

Question 8

8. 𝑑/𝑑𝑥 [𝑒𝑥] = 𝑒𝑥

Question 9

9. 𝑑/𝑑𝑥 [𝑎𝑥] = 𝑎𝑥 ln 𝑎

Question 10

10. 𝑑/𝑑𝑥 [ln 𝑥] =1/𝑥

Question 11

11. 𝑑/𝑑𝑥 [log𝑎 𝑥] =1/𝑥 ln 𝑎

Question 12

12. 𝑑/𝑑𝑥 [sin 𝑥] = cos 𝑥

Question 13

13. 𝑑/𝑑𝑥 [cos 𝑥] = − sin 𝑥

Question 14

14. 𝑑/𝑑𝑥 [tan 𝑥] = sec2 𝑥

Question 15

15. 𝑑/𝑑𝑥 [cot 𝑥] = − csc2 𝑥

Question 16

16. 𝑑/𝑑𝑥 [sec 𝑥] = sec 𝑥 tan 𝑥

Question 17

17. 𝑑/𝑑𝑥 [csc 𝑥] = − csc 𝑥 cot 𝑥